Abstract

By analyzing the nonlinear optical response in an asymmetric coupled double quantum well structure based on the intersubband transitions, we show that a giant Kerr nonlinearity with a relatively large cross-phase modulation coefficient can be used to produce efficient photonphoton entanglement and implement an all-optical two-qubit quantum polarization phase gate. We also demonstrate that such photon-photon entanglement is practically controllable and may facilitate more practical applications in all-optical quantum information and computation.

©2008 Optical Society of America

There have been many progresses in the development of logic gates and memory devices using nonlinear optical effects, especially with the resonant semiconductor optical nonlinearities [1]. Resonant optical nonlinearities in semiconductors occur at the small intensity and small current, with a controllable flexibility. But the spectral overlap of the absorption and corresponding refractive index changes must be taken into account for such device designs. The existence of the electromagnetically induced transparency (EIT) in systems of semiconductor quantum well (SQW) structures is of particular significance because EIT and EIT-related phenomena have been proven to have a vast number of important applications in cold atom gases [2, 3, 4, 5, 6, 7] and hence received considerable attentions in the past decades. It opens up an avenue to explore new possibilities for nonlinear optics and related quantum information processing (QIP) via EIT. It is more advantageous at least from the view point of practical purposes to find, instead of above mentioned cold atom gases, SQW solid systems to realize giant cross phase modulation (XPM) phase shifts and the related QIP with merits such as large electric dipole moments due to the small effective electron mass, high nonlinear optical coefficients, and a great flexibility in device design by choosing the materials and structure dimensions. Besides, in SQW devices the transition energies, dipoles, and symmetries can also be controlled at will. More importantly, the SQW structure also provides another possibility to realize electrically controlled phase modulators and QIP due to that the conduction subband energy level can be easily tuned by an external bias voltage [8, 9]. In this regards, we note that EIT [10, 11], tuneling-induced transparency (TIT) [9], ultrafast switching [12], slow light [8, 13, 14], optical solitons [15], optical delay [16], etc, have been investigated in SQW systems. However, as far as we know, up to now no any work has explored Kerr nonlinearity and its applications for producing entangled-photon states and all-optical quantum phase gate (QPG) based on EIT effect in SQW systems.

 figure: Fig. 1.

Fig. 1. (a) Schematic band diagram of the asymmetric CQW structure consisting of a wide well (WW) and a narrow well (NW). (b) Schematic of the four-level electronic system synthesized in CQW structure. Ωp (σ +polarization), Ωs (σ-polarization), and Ωc are the Rabi frequencies of the probe, signal, and cw control fields, respectively. The Δi j denotes the corresponding detunings. (c) Possible arrangement of experimental apparatus. Ec represents the control field and Ep (Es) represents the σ+(σ-) polarized probe (signal) field, respectively.

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In this work, we propose a scheme to produce entangled-photon states and implement an all-optical two-qubit QPG through a four-subbandN-type system in an asymmetric coupled double quantum well (CQW) structure based on intersubband transitions (ISBT). First, we analyze the nonlinear optical response of the proposed scheme and obtain the optimal conditions to enhance the cross-Kerr nonlinearity significantly and the related XPM with the suppressing of absorption in the medium. Then we study the entangled-photon states and the possibility of employing such enhanced XPM to construct an all-optical two-qubit QPG, in which the binary quantum information is encoded by using the polarization degree of freedom of the probe and signal fields. The results we have obtained here may facilitate more practical applications for QIP in solid media.

1. Model for couple double quantum wells

Let us consider an asymmetric CQW structure [17] consisting of a wide well (WW) and a narrow well (NW) as shown in Fig. 1, where level |1〉 and level |2〉 are localized hole states in the valence band. And level |3〉 and level |4〉 are delocalized electronic states extended between the wells in the conduction band (a bonding state and an antibonding one), which arise due to the tunneling effect. The system interacts with a weak pulsed probe field of center frequency ωp, a weak pulsed signal field of frequency ωs, and a strong continuous wave (cw) control field of frequency ωc. The Rabi frequencies associated with the lasers driving the transitions are defined as Ωk=µijEk/h̄(i, j=1,2,3,4 and i≠j), with Ek, µij being the corresponding electric field amplitude and the relative dipole matrix element induced on the transition |i〉↔|j〉, respectively. The detunings Δij (see Fig. 1) are defined as: Δ13=E3/h̄-ωp, Δ23=(E3-E2)/h̄-ωc, and Δ24=(E 4-E 2)/h̄-ωs. Here we have taken E 1=0 for the ground state level |1〉as the energy origin. This CQW structure can be consisted of 10 pairs of a 51-monolayer (145 Å) thick wide well and a 35-monolayer (100Å) thick narrow well, separated by an Al0.2Ga0.8As buffer layer. The first (n=1) electron levels in the wide well and the narrowwell can be energetically aligned with each other by applying a static electric field, while the corresponding n=1 hole levels are never aligned along this polarization direction of the field. The electrons then delocalize over both wells while the holes remain localized. For transitions from the narrow well and wide well, the Coulomb interaction between the electron and the hole down shifts the value of the electric field, where the resonance condition is fulfilled to the corresponding built-in field. Such a CQW system has been intensively studied previously but in different context [18, 19, 20]. In the present analysis we use the following conditions: (i) The semiconductor quantum wells with low doping are designed such that electron-electron effects have very small influence in our results. As a result, many-body effects arising from electron-electron interactions are not included in our study. (ii) We assume that all subbands have the same effective mass. Working in the interaction picture, utilizing the rotating-wave approximation (RWA) and the electric-dipole approximation (EDA), the dynamics of our system can be described by equations of motion for the probability amplitudes of the electronic wave functions,

iA1t=Ωp*A3,
iA2t=(Δ23iγ22)A2+Ωc*A3+Ωs*A4,
iA3t=(Δ13iγ32)A3+ΩpA1+ΩcA2+iκA4,
iA4t=(Δ24iγ42)A4+ΩsA2+iκA3,

together with Aj(j=2,3,4) being the amplitudes of subbands |j〉. The parameters γ 2,3,4 are added phenomenologically to describe the corresponding decay rates of subbands |2〉, |3〉 and |4〉. The total decay rate γi (γi=γil+γ dph i) of subband |i〉 comprises a population-decay contribution γil, primarily due to the longitudinal optical (LO) phonon emission events at low temperature, and a dephasing contribution γdphi, determined by electron-electron scattering, interface roughness, and phonon scattering processes. The population decay rates can be calculated by solving the effective mass Schrödinger equation. For the temperatures up to 10 K, the electric sheet density kept below 5×1011 cm-2 per double well to minimize dephasing from carrier scattering [17], the dephasing decay rates γ dphi j can be estimated according to Refs. [21, 22]. κ=γ3lγ4l denotes the mutual coupling of states |3〉 and |4〉 via the LO phonon decay; it describes the process in which a phonon is emitted by subband |3〉 and recaptured by subband |4〉. Such behavior is similar to the decay-induced interference in atomic systems with two closely lying energy states [9].

2. Giant cross-Kerr nonlinearity and group velocity matching

We assume that the initial state of the system is in the ground state |1〉. Note that if the intensities of the probe and signal fields are much weaker than that of the control field, we can neglect the decay of the ground state due to the quantum coherence and interference effects, thus we can have A 1 ≈ 1. In other words, the pumping effect among different ground state levels can be neglected during the evolution of the system because almost all electrons will remain in the subband level |1〉. In order to solve Eqs. (1-4), we assume that the typical operation time durations of the probe and signal fields are long enough so that a steady state approximation can be employed. To obtain the expressions for nonlinear optical susceptibilities of this system we consider higher order contributions to A 1, which can be obtained by using the normalization condition ∑4 j=1|Aj|2 ≈ 1. By solving Eqs. (1-4) under these conditions, one can obtain

Aj=2,3,4=(cΩc*iΩs*κ)δj2+(bc+Ωs2)δj3+(ibκΩc*Ωs)δj4abc+bκ2aΩs2cΩc2+iκ(Ωc*Ωs+ΩcΩs*)Ωp,
where a13-iγ3/2, b23-iγ2/2, and c24- 4/2. From above values of A2, A3, and A4, we can obtain the following expressions for the susceptibilities of probe and signal fields, χp and χs, respectively [23],

χp=Nμ132h̄ε0A3A1*Ωpχp(1)+χp(3,S)Ep2+χp(3,C)Es2,
χs=Nμ242h̄ε0A4A2*Ωsχs(3,C)Ep2,

where N is the electron density in the conduction band of quantum well and ε 0 is the vacuum dielectric constant. χ(1)p, χ(3,S)p, and χ(3,C)p are respectively the linear susceptibility, third-order nonlinear susceptibilities characterizing the effect of self-Kerr and cross-Kerr nonlinearities of the probe field, and χ(3,C)s is the third-order cross-Kerr nonlinear susceptibility of the signal field.

 figure: Fig. 2.

Fig. 2. The real and imaginary parts of (a) the linear susceptibility χ(1)p=N|µ13|2/h̄ε0χ′(1)p, and (b) third-order self-Kerr susceptibility χ(3,S)p=N|µ13| 4/h̄3ε0χ′(3,S)p versus the detuning of the probe field Δ13 (in the unit of meV). Other parameters used here are given by γ2=0, γ3l=γ4l=3.5meV, γdph3=γ dph4=1.5meV, Δ24=8meV, Ωc=25meV, and Ωs=2.5meV.

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With suitable parameters, the associated cross-Kerr susceptibilities χ(3,C)p and χ(3,C)s can be greatly enhanced under EIT condition. We show in Fig. 2 the linear and self-Kerr susceptibilities versus the probe field for various detunings Δ13 under the EIT condition, which illustrates the EIT response of a ”Λ-type” subsystem. In the case of resonance of the probe field Ω p13=0), the Λ subsystem forms an dark state where the real and the imaginary parts of both χ(1)p and χ(3,S)p vanish. Fig. 3 shows the dependence of the third-order cross-Kerr susceptibilities, χ(3,C)p and χ(3,C)s, on the detuning of the signal field Ωs with the resonance condition of the fields Ωp and Ωc (i.e., Δ1323=0). From Fig. 3, one can find that the real parts of the two cross-Kerr susceptibilities decay much more slowly than the imaginary parts within the transparency window. Therefore, when the signal field is relatively far off resonance we can achieve an appreciable XPM phase shift with a negligible absorption. Besides, it is observed that the two cross-Kerr susceptibilities are of the same order of magnitudes. Although it is well known that a similar N-type scheme is analyzed in the cold atom system [7, 24], but different from other systems (such as cold atom gases), here we can obtain very large dipole moments for the ISBT in our CQW system [17, 18, 19]. For a certain detuning Δ24=10 meV, it can be calculated that the real part of cross-Kerr susceptibility is about 10-10m2V-2, which is much larger than that can be achieved in microstructured optical fibers (about 10-22m2V-2) [23] and in cold atom systems (about 10-14m2V-2) [24]. Importantly, this is achieved with the linear and self-Kerr interactions vanish simultaneously. This interesting results are produced by the quantum coherence and interference between the lower states under the EIT condition. In addition, one can readily checked that the decay-induced interference, κ, only has a small effect on the XPM because here the XPM is mainly induced by the control field Ωc under the condition κ ≪ Ωc.

 figure: Fig. 3.

Fig. 3. The real and imaginary parts of the third-order cross-Kerr susceptibilities for (a) the probe field χ(3,C)p=N13|224|2/h̄3ε0χ′(3,C)p, and (b) the signal field χ(3,C)s=N13|224|2/h̄3ε0χ′(3,C)s versus the detunings Δ24 (in the unit of meV) at the center of EIT window. Other parameters used are the same as those in Fig. 2.

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It should be emphasized that group velocity matching is another necessary condition to achieve a large mutual phase shift because only in this way can the probe and signal optical pulses interact for a sufficiently long time in a transparent nonlinear medium [4]. The group velocity of an optical pulse is given by νg=c/(1+ng), where c is the speed of light in vacuum, and the group index is given by

(ng)i=Re[χ]+(ωi2)(Re[χ]ω)ωi

with ωi(i=p, s) being the laser frequency. We assume that the probe field works at the center of EIT window (i.e., Δ2313=0). Two group velocities, (νg)p and (νg)s, can be made both small and equal by properly adjusting the Rabi frequencies, dipole moments, and detunings. According to the parameters setting above, we show in Fig. 4 the dimensionless group velocities (νg)p,s of the probe and signal fields versus the detuning Δ24, with Ωp=4.2 meV and Ωs=2.5 meV. From Fig. 4, one can find that the group velocities of two fields can be matched approximately within the range of detunings 9 ≤ Δ24 ≤ 10 meV. As shown in the Fig. 4, the group velocities of both probe and signal fields are reduced with the order of 10 2 in a small range of Δ24. From Fig. 1(b), one can find that Ωp, Ωc, and the three levels |1〉, |2〉, |3〉, form a Λ subsystem of the regular EIT configuration. The probe light Ω p can propagate slowly in this condition. Even there is no population (or negligible population) in state |2〉, the energy level |2〉 will be modulated by the strong coupling field Ωc [25], which will result in the dispersion of field Ωs. Both Ωp and Ωc will contribute to the dispersion, just as Ωs can affect the dispersion of the probe field Ωp [26]. Besides, we can obtain large dipole moments in our CQW structure. Thus matched slow light output can exist through suitable parameters.

 figure: Fig. 4.

Fig. 4. Dimensionless group velocities (νg)p,s/ν of the probe and signal fields versus the detunings of the signal field Δ24 (in the unit of meV) for ν=106m/s, in which the solid and dashed lines denote the probe and signal fields, respectively.

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3. Controllable entanglement and two-qubit phase gate

In this section, we demonstrate that such third-order cross-Kerr nonlinearity can be used to implement a 2-qubit controlled QPG. A 2-qubit QPG operation can be expressed as |i〉1|j2→expij|i〉1|j〉2, where i, j=0,1 denote the logical qubit basis. The binary information in our system is encoded by using the polarization degree of freedom in the probe and signal pulses. We assume the four-state system shown Fig. 1 is implemented when the probe field has σ +polarization and the signal one has polarizationσ ̄. If either (both) the probe or (and) the signal polarizations are changed, the phase shifts acquired by two pulses do not involve the cross-Kerr nonlinearity and lead to a difference. Specifically, when probe field has a “wrong” polarizations (σ̄-polarized) there is no sufficiently close excited state to which the subbands can be coupled and the two fields acquire only the trivial phase shift ϕi0=kiL (i=p, s) in vacuum, where L is the length of the medium and ki=ωi/c denotes the free space wave vector. When probe and signal fields are both σ +-polarized, the probe field, subject to the EIT condition produced by the Λ configuration of |1〉-|2〉-|3〉 subbands, experiences a self-Kerr effect and acquires a nontrivial phase shift ϕpΛ=ϕp0p1p3,S, with ϕp1=2πkp(1)p being the linear phase shift and ϕp3,S begin the nonlinear phase shift induced by self-Kerr nonlinearity (i.e. the self-phase modulation). Moreover, the signal acquires again the vacuum phase shift ϕ s0. When both of them have the ”right” polarizations (probe σ +-polarized and signal σ --polarized), the probe and signal fields acquire nontrivial phase shifts ϕptotal=ϕpΛ+ϕp3,C and ϕ stotalsΛ+ϕ s3,C, respectively. The nonlinear shifts ϕ p3,C and ϕ s3,C induced by the cross-Kerr nonlinearity (i.e. XPM) are given by

ϕ3,Cp=kpLπ32h̄2Ωspeak24μ242erf[ζp]ζpRe[χp(3,C)],
ϕ3,Cs=ksLπ32h̄2Ωppeak24μ132erf[ζs]ζsRe[χs(3,C)],

where ζp=(1-(vg)p/(vg )s)√2L/(vg)pτs, and ζs can be obtained from ζp upon interchanging the indices p⃡s. Here er f[ζ] denotes the error function, and τi(i=p, s) is the time duration of the pulse. Large nonlinear XPM phase shifts take place for appreciably large values of the real parts of two cross-Kerr susceptibilities, especially when the group velocities of probe and signal fields matched, i.e. as ζp,s→0, the value of er f[ζi]/ζi reaches the maximum value 2/√π. The truth table for a polarization 2-qubit QPG using our CQW structure reads in the following,

0p0sexp[i(ϕ0p+ϕ0s)]0p0s,
0p1sexp[i(ϕ0p+ϕ0s)]0p1s,
1p1sexp[i(ϕΛp+ϕ0s)]1p1s,
1p0sexp[i(ϕtotalp+ϕ0s)]1p0s.

Here we have encoded |σi→|0i and |σ+i→|1〉i, and the conditional phase shift is ϕcon=ϕptotal+ϕstotal-ϕpΛ-ϕs0. Based on the above analysis, the linear effect and self-phase modulation can be suppressed when ϕpΛ=ϕp0, i.e. ϕptotal=ϕp0 +ϕp3,C, ϕstotal=ϕs0+ϕs3,C, and ϕcon=ϕp3,c+ϕs3,C. In this case, only the third order nonlinear phases in Eqs. (9) and (10) contribute to the conditional phase shift ϕcon. Thus we have realized a 2-qubit polarization phase gate operation in the CQW structure.

 figure: Fig. 5.

Fig. 5. The concurrence versus the detuning of the signal field (in the unit of meV) for two different Rabi frequencies of control field.

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We now turn to the problem of entangled-photon states in our quantum well system. Here we use the entanglement of formation as a measurement of the purity in our two polarized photons state. For an arbitrary two-qubit system, the degree of entanglement is defined by [27]

EF(C)=h(1+1C22),

where h(x)=-xlog2(x)-(1-x)log2(1-x) is Shannon entropy function, and the so called ”concurrence”,C, is given by

C(ρ̂)=max{0,λ1λ2λ3λ4},

with λi(i=1,2,3,4) being the square roots of the eigenvalues, in a decreasing order, for the matrix ρ̂σ^ pyσ^ sy ρ^ *σ^ pyσ^ sy. Here ρ̂* denotes the complex conjugation of the output state density matrix ̂ ρ, and ̂ σiy (i=p, s) is the y-component of the Pauli matrix. EF(C) is a monotonic function of C, thus we can also use the concurrence directly as our measurement of entanglement. It should be emphasized that the entanglement can be controlled by adjusting the related parameters of the system. As an example, we plot in Fig. 5 the concurrence as a function of the detuning Δ24 in the unit of meV. For the sake of simplicity, we take the value of N13|2ωp/2h̄ε0c=N24|2 ωs/2h̄ε0c=105meV/cm and the length of the medium L ≈2 mm as an example. The probe and signal fields have a mean amplitude about one photon when the beams are tightly focused. For a certain detuning of the signal field (Δ24=10 meV), we obtain the degree of entanglement EF ≈ 31% with the conditional phase shift ϕconπ at the same time. By choosing an appropriate detuning, the maximum degree of entanglement obtained in our proposal can be as large as 35%. It is worth to note that the fluctuations of light intensities and the detunings of probe and signal fields will result in errors of measurement of the nonlinear phase shift in the experimental demonstration.

4. Discussion and conclusion

Just as done before [12, 15, 20], we analyzed the nonlinear response by using the one-dimensional model in calculation and neglected the momentum dependency of subband energies. However, there is no large discrepancy between the reduced one-dimensional and a full two-dimensional calculations [12]. In addition, we have not used the density matrix formalism including the decay rates to describe the system. It can readily be checked by numerical simulations that the results of the treatment here are essentially the same as those from the usual density matrix formalism [24, 28].

Before conclusion, we should note that we have neglected other additional broadening induced by the carrier-carrier and carrier-photon interactions. In the present one-dimensional model, the effects of additional broadening can be included by first rewriting the corresponding detunings, i.e., Δij=(Ej-Ei)/h̄-ωs,p,c as Δijad with Δad being the additional broadening effects. According to the Ref. [29], we find that even for the moderate density at 300K, additional broadening effects are on the order of 1 meV, which is very small compared with the final linewidth even at room temperature. Besides, some other many-body effects also contribute to the broadening, for example, the depolarization effect, which renormalizes the free-carrier and carrier-field contributions [30, 31]. Due to the small electron sheet density considered here, these effects only give a small extent.

In conclusion, we have analyzed the nonlinear response of an asymmetric CQW structure based on the intersubband transitions (ISBT). Under the condition Δ1323=0, we have shown that the cross-Kerr susceptibilities can greatly enhanced while the linear and the self-Kerr nonlinear susceptibilities are simultaneously suppressed due to the quantum interference effect induced by a strong cw control laser field. Based on such important features we have studied the entanglement between two weak lights and explored the possibility to implement a robust two-qubit QPG with the given system.

In the literature several four- or multiple-level structures in atomic systems, such as ”M-type” or ”Y-type”, have been proposed to investigate the Kerr nonlinearities [4, 5, 6]. Even in CQW system, this is achieved by mapping the model describing the four subbands interacting with the three laser fields into the model describing the nonlinear response through the gas of four-level cold atoms [7, 24, 28]. However, there are some crucial differences between these two situations, with important implications to be explained shortly. First, the medium studied here is a solid, which is much more practical than that in gaseous media due to its flexible design and the controllable interference strength. Second, the transition energies, dipoles, and symmetries can be controlled at will. For instance, the XPM phase shifts obtained here and the condition of the group velocity matching can be conveniently adjusted within a large range of parameters in a typical CQW system while they can hardly be found in the models for cold atom media. What is more important, the results obtained in the present study may be useful for guiding experimental realization of electroptically modulated devices and facilitating more practical applications in solid quantum information and computation.

Acknowledgment

We would like to thank Ite. Yu and KaiJun. Jiang for many helpful discussions. The research is supported in part by the National Science Council of Taiwan under the contract number 95-2112-M-007-058-MY3and NSC-95-2120-M-001-006. WXY is also supported by National Natural Science Foundation of China under Grant Nos. 10704017 and 10575040, by National Fundamental Research Program of China 2005CB724508.

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29. I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004). [CrossRef]  

30. D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997). [CrossRef]  

31. E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006). [CrossRef]  

References

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  1. H. C. Liu and F. Capasso, “Intersubband Transitions in Quantum Wells: Physics and Device Applications,” (Academic Press, 2000).
  2. K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
    [Crossref] [PubMed]
  3. S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today  50, 36–42 (1997).
  4. C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
    [Crossref]
  5. A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
    [Crossref]
  6. C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
    [Crossref]
  7. H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
    [Crossref] [PubMed]
  8. P. Ginzburg and M. Orenstein, “Slow light and voltage control of group velocity in resonantly coupled quantum wells,” Opt. Express 14, 12467–12472 (2006).
    [Crossref] [PubMed]
  9. H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
    [Crossref]
  10. C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
    [Crossref]
  11. L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
    [Crossref]
  12. J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
    [Crossref]
  13. P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
    [Crossref] [PubMed]
  14. P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
    [Crossref] [PubMed]
  15. W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
    [Crossref]
  16. S. Sarkar, Y. Guo, and H. Wang, “Tunable optical delay via carrier induced exciton dephasing in semiconductor quantum wells,” Opt. Express 14, 2845–2850 (2006).
    [Crossref] [PubMed]
  17. H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
    [Crossref] [PubMed]
  18. M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
    [Crossref]
  19. P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
    [Crossref]
  20. J. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
    [Crossref]
  21. J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).
  22. J. Faist, C. Sirtori, F. Capasso, S.-N. G. Chu, L. N. Pfeiffer, and K. W. West, “Tunable Fano interference in intersubband absorption,” Opt. Lett. 21, 985–988 (1996).
    [Crossref] [PubMed]
  23. G. P. Agrawal, “Nonlinear fiber optics,” (3rd ed.Academic Press, New York, 2001).
  24. Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
    [Crossref]
  25. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
    [Crossref]
  26. H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
    [Crossref]
  27. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
    [Crossref]
  28. Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
    [Crossref]
  29. I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
    [Crossref]
  30. D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
    [Crossref]
  31. E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
    [Crossref]

2008 (1)

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[Crossref]

2007 (1)

J. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
[Crossref]

2006 (5)

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[Crossref]

S. Sarkar, Y. Guo, and H. Wang, “Tunable optical delay via carrier induced exciton dephasing in semiconductor quantum wells,” Opt. Express 14, 2845–2850 (2006).
[Crossref] [PubMed]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[Crossref]

P. Ginzburg and M. Orenstein, “Slow light and voltage control of group velocity in resonantly coupled quantum wells,” Opt. Express 14, 12467–12472 (2006).
[Crossref] [PubMed]

2005 (4)

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
[Crossref]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[Crossref]

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[Crossref] [PubMed]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[Crossref]

2004 (5)

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[Crossref]

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
[Crossref]

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
[Crossref]

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
[Crossref] [PubMed]

2003 (1)

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[Crossref]

2002 (1)

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[Crossref]

2000 (1)

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[Crossref]

1998 (1)

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[Crossref]

1997 (3)

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[Crossref]

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today  50, 36–42 (1997).

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[Crossref]

1996 (2)

1993 (2)

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[Crossref]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[Crossref]

1992 (1)

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

1991 (1)

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Agrawal, G. P.

G. P. Agrawal, “Nonlinear fiber optics,” (3rd ed.Academic Press, New York, 2001).

Artoni, M.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[Crossref]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[Crossref]

Bassani, F.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[Crossref]

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[Crossref]

Boller, K. J.

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Brener, I.

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[Crossref]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[Crossref]

Butov, L. V.

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[Crossref]

Campman, K. L.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[Crossref]

Capasso, F.

J. Faist, C. Sirtori, F. Capasso, S.-N. G. Chu, L. N. Pfeiffer, and K. W. West, “Tunable Fano interference in intersubband absorption,” Opt. Lett. 21, 985–988 (1996).
[Crossref] [PubMed]

H. C. Liu and F. Capasso, “Intersubband Transitions in Quantum Wells: Physics and Device Applications,” (Academic Press, 2000).

Cataliotti, F.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[Crossref]

Chang, S. W.

Chang-Hasnain, C.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[Crossref] [PubMed]

Chang-Hasnain, C. J.

Chu, S.-N. G.

Chuang, S. L.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
[Crossref] [PubMed]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[Crossref]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[Crossref]

Crankshaw, S.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[Crossref] [PubMed]

Czajkowski, G.

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[Crossref]

Davoudi, B.

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[Crossref]

Deng, L.

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
[Crossref]

Dynes, J. F.

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).

Elsaesser, T.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Faist, J.

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[Crossref]

Forstner, J.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Fox, A.M.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

Gao, J.-Y.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[Crossref]

Ginzburg, P.

Gossard, A. C.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[Crossref]

Guo, Y.

Hang, C.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[Crossref]

Harris, S. E.

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today  50, 36–42 (1997).

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Hernandez, G.

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[Crossref]

Hey, R.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Hou, J. M.

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[Crossref]

Huang, G.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[Crossref]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[Crossref]

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[Crossref]

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[Crossref]

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[Crossref] [PubMed]

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Joshi, A.

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
[Crossref]

Kaindl, R. A.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Kang, H.

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[Crossref]

Knorr, A.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Kohler, K.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

Ku, P. C.

La Rocca, G. C.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[Crossref]

Lee, R.-K.

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[Crossref]

Lee, S.-C.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Leo, K.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

Li, J.

J. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
[Crossref]

Li, T.

Li, Y.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[Crossref]

Liu, H. C.

H. C. Liu and F. Capasso, “Intersubband Transitions in Quantum Wells: Physics and Device Applications,” (Academic Press, 2000).

Luo, M. S. C.

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[Crossref]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[Crossref]

Ma, L.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[Crossref]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[Crossref]

Miller, D. A. B.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

Moewe, M.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[Crossref] [PubMed]

Nikonov, D. E.

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[Crossref]

Nuss, M. C.

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[Crossref]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[Crossref]

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

Orenstein, M.

Ottaviani, C.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[Crossref]

Palinginis, P.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[Crossref] [PubMed]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
[Crossref] [PubMed]

Paspalakis, E.

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[Crossref]

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[Crossref]

Pfeiffer, L. N.

Phillips, C. C.

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[Crossref]

Planken, P. C. M.

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[Crossref]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[Crossref]

Ploog, K. H.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Reimann, K.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Roskos, H. G.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

Sarkar, S.

Schmidt, H.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[Crossref]

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[Crossref]

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[Crossref] [PubMed]

Schmitt-Rink, S.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

Sedgwick, F.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[Crossref] [PubMed]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
[Crossref] [PubMed]

Serapiglia, G. B.

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[Crossref]

Shah, J.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

Silvestri, L.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[Crossref]

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[Crossref]

Sirtori, C.

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[Crossref]

J. Faist, C. Sirtori, F. Capasso, S.-N. G. Chu, L. N. Pfeiffer, and K. W. West, “Tunable Fano interference in intersubband absorption,” Opt. Lett. 21, 985–988 (1996).
[Crossref] [PubMed]

Terzis, A. F.

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[Crossref]

Tombesi, P.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[Crossref]

Tsaousidou, M.

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[Crossref]

Vitali, D.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[Crossref]

Vodopyanov, K. L.

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[Crossref]

Waldmüller, I.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Wang, H.

West, K. W.

Woerner, M.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

Wootters, W. K.

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[Crossref]

Wu, J.-H.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[Crossref]

Wu, Y.

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
[Crossref]

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
[Crossref]

Xiao, M.

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
[Crossref]

Xu, J.-H.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[Crossref]

Yang, W. X.

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[Crossref]

Yang, X.

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
[Crossref]

Zhu, Y. F.

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[Crossref]

Appl. Phys. Lett. (1)

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[Crossref]

Eur. Phys. J. B (1)

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[Crossref]

Opt. Commun. (1)

J. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
[Crossref]

Opt. Express (2)

Opt. Express. (1)

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. (1)

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today  50, 36–42 (1997).

Phys. Rev. A (6)

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
[Crossref]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[Crossref]

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[Crossref]

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[Crossref]

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
[Crossref]

Phys. Rev. B (4)

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[Crossref]

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[Crossref]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[Crossref]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[Crossref]

Phys. Rev. Lett. (7)

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
[Crossref]

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[Crossref]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[Crossref]

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[Crossref] [PubMed]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[Crossref]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[Crossref]

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[Crossref] [PubMed]

Physica E (1)

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[Crossref]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[Crossref]

Other (2)

G. P. Agrawal, “Nonlinear fiber optics,” (3rd ed.Academic Press, New York, 2001).

H. C. Liu and F. Capasso, “Intersubband Transitions in Quantum Wells: Physics and Device Applications,” (Academic Press, 2000).

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic band diagram of the asymmetric CQW structure consisting of a wide well (WW) and a narrow well (NW). (b) Schematic of the four-level electronic system synthesized in CQW structure. Ω p (σ +polarization), Ω s (σ-polarization), and Ω c are the Rabi frequencies of the probe, signal, and cw control fields, respectively. The Δ i j denotes the corresponding detunings. (c) Possible arrangement of experimental apparatus. Ec represents the control field and Ep (Es ) represents the σ+ (σ-) polarized probe (signal) field, respectively.
Fig. 2.
Fig. 2. The real and imaginary parts of (a) the linear susceptibility χ(1)p=N|µ13|2/h̄ε0χ′(1)p, and (b) third-order self-Kerr susceptibility χ(3,S)p=N|µ13| 4/h̄3ε0χ′(3,S)p versus the detuning of the probe field Δ13 (in the unit of meV). Other parameters used here are given by γ2 =0, γ3l =γ4l =3.5meV, γdph3=γ dph4=1.5meV, Δ24=8meV, Ω c =25meV, and Ω s =2.5meV.
Fig. 3.
Fig. 3. The real and imaginary parts of the third-order cross-Kerr susceptibilities for (a) the probe field χ(3,C) p =N13|224|2/h̄3ε0χ′(3,C)p, and (b) the signal field χ(3,C)s=N13|224|2/h̄3ε0χ′(3,C)s versus the detunings Δ24 (in the unit of meV) at the center of EIT window. Other parameters used are the same as those in Fig. 2.
Fig. 4.
Fig. 4. Dimensionless group velocities (νg ) p,s /ν of the probe and signal fields versus the detunings of the signal field Δ24 (in the unit of meV) for ν=106m/s, in which the solid and dashed lines denote the probe and signal fields, respectively.
Fig. 5.
Fig. 5. The concurrence versus the detuning of the signal field (in the unit of meV) for two different Rabi frequencies of control field.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

i A 1 t = Ω p * A 3 ,
i A 2 t = ( Δ 23 i γ 2 2 ) A 2 + Ω c * A 3 + Ω s * A 4 ,
i A 3 t = ( Δ 13 i γ 3 2 ) A 3 + Ω p A 1 + Ω c A 2 + i κ A 4 ,
i A 4 t = ( Δ 24 i γ 4 2 ) A 4 + Ω s A 2 + i κ A 3 ,
A j = 2 , 3 , 4 = ( c Ω c * i Ω s * κ ) δ j 2 + ( b c + Ω s 2 ) δ j 3 + ( i b κ Ω c * Ω s ) δ j 4 a b c + b κ 2 a Ω s 2 c Ω c 2 + i κ ( Ω c * Ω s + Ω c Ω s * ) Ω p ,
χ p = N μ 13 2 h ̄ ε 0 A 3 A 1 * Ω p χ p ( 1 ) + χ p ( 3 , S ) E p 2 + χ p ( 3 , C ) E s 2 ,
χ s = N μ 24 2 h ̄ ε 0 A 4 A 2 * Ω s χ s ( 3 , C ) E p 2 ,
( n g ) i = Re [ χ ] + ( ω i 2 ) ( Re [ χ ] ω ) ω i
ϕ 3 , C p = k p L π 3 2 h ̄ 2 Ω s peak 2 4 μ 24 2 e r f [ ζ p ] ζ p R e [ χ p ( 3 , C ) ] ,
ϕ 3 , C s = k s L π 3 2 h ̄ 2 Ω p peak 2 4 μ 13 2 e r f [ ζ s ] ζ s R e [ χ s ( 3 , C ) ] ,
0 p 0 s exp [ i ( ϕ 0 p + ϕ 0 s ) ] 0 p 0 s ,
0 p 1 s exp [ i ( ϕ 0 p + ϕ 0 s ) ] 0 p 1 s ,
1 p 1 s exp [ i ( ϕ Λ p + ϕ 0 s ) ] 1 p 1 s ,
1 p 0 s exp [ i ( ϕ total p + ϕ 0 s ) ] 1 p 0 s .
E F ( C ) = h ( 1 + 1 C 2 2 ) ,
C ( ρ ̂ ) = max { 0 , λ 1 λ 2 λ 3 λ 4 } ,

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