Abstract

Creating stable superposed states of matter is one of the most intriguing aspects of quantum physics, leading to a variety of counterintuitive scenarios along with a possibility of restructuring the way we understand, process, and communicate information. Accordingly, there has been a major research thrust in understanding and quantifying such stable superposed states. Here, we propose and experimentally explore a quantifier that captures effective quantum coherence in an atomic ensemble at room temperature. The quantifier provides direct measure of ground-state coherence for electromagnetically induced transparency (EIT) along with a distinct signature of transition from EIT to Autler–Townes splitting regime in the ensemble. Using the quantifier as an indicator, we further demonstrate a mechanism to coherently control and freeze coherence by introducing an active channel that compensates decay in the system. In the growing pursuit of quantum technologies at room temperature, our results provide a unique way to phenomenologically quantify and coherently control quantum coherence in atom-like systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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Discerning electromagnetically induced transparency from Autler-Townes splitting in plasmonic waveguide and coupled resonators system

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    [Crossref]
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    [Crossref]
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    [Crossref]
  44. L. Yang, L. Zhang, X. Li, L. Han, G. Fu, N. B. Manson, D. Suter, and C. Wei, “Autler-Townes effect in a strongly driven electromagnetically induced transparency resonance,” Phys. Rev. A 72, 053801 (2005).
    [Crossref]
  45. C. Y. Ye, A. S. Zibrov, Y. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A 65, 043805 (2002).
    [Crossref]
  46. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
    [Crossref]
  47. G. S. Agarwal, T. N. Dey, and S. Menon, “Knob for changing light propagation from subluminal to superluminal,” Phys. Rev. A 64, 053809 (2001).
    [Crossref]
  48. H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80, 023820 (2009).
    [Crossref]
  49. M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50, 165502 (2017).
    [Crossref]
  50. M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: theory,” Phys. Rev. A 74, 013812 (2006).
    [Crossref]
  51. M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity,” Phys. Rev. A 76, 033835 (2007).
    [Crossref]
  52. R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5, 100–104 (2009).
    [Crossref]
  53. H. G. Barros, A. Stute, T. E. Northup, C. Russo, P. O. Schmidt, and R. Blatt, “Deterministic single-photon source from a single ion,” New J. Phys. 11, 103004 (2009).
    [Crossref]

2017 (5)

A. Streltsov, G. Adesso, and M. B. Plenio, “Colloquium: quantum coherence as a resource,” Rev. Mod. Phys. 89, 041003 (2017).
[Crossref]

Y.-T. Wang, J.-S. Tang, Z.-Y. Wei, S. Yu, Z.-J. Ke, X.-Y. Xu, C.-F. Li, and G.-C. Guo, “Directly measuring the degree of quantum coherence using interference fringes,” Phys. Rev. Lett. 118, 020403 (2017).
[Crossref]

P. Neveu, M.-A. Maynard, R. Bouchez, J. Lugani, R. Ghosh, F. Bretenaker, F. Goldfarb, and E. Brion, “Coherent population oscillation-based light storage,” Phys. Rev. Lett. 118, 073605 (2017).
[Crossref]

M. K. Bhaskar, D. D. Sukachev, A. Sipahigil, R. E. Evans, M. J. Burek, C. T. Nguyen, L. J. Rogers, P. Siyushev, M. H. Metsch, H. Park, F. Jelezko, M. Lončar, and M. D. Lukin, “Quantum nonlinear optics with a germanium-vacancy color center in a nanoscale diamond waveguide,” Phys. Rev. Lett. 118, 223603 (2017).
[Crossref]

M. Ghosh, A. Karigowda, A. Jayaraman, F. Bretenaker, B. C. Sanders, and A. Narayanan, “Demonstration of a high-contrast optical switching in an atomic delta system,” J. Phys. B 50, 165502 (2017).
[Crossref]

2016 (4)

X. Gu, S.-N. Huai, F. Nori, and Y.-X. Liu, “Polariton states in circuit QED for electromagnetically induced transparency,” Phys. Rev. A 93, 063827 (2016).
[Crossref]

P. Hauke, M. Heyl, L. Tagliacozzo, and P. Zoller, “Measuring multipartite entanglement through dynamic susceptibilities,” Nat. Phys. 12, 778–782 (2016).
[Crossref]

D. Suter and G. A. Álvarez, “Colloquium: protecting quantum information against environmental noise,” Rev. Mod. Phys. 88, 041001 (2016).
[Crossref]

A. W. Laskar, N. Singh, A. Mukherjee, and S. Ghosh, “Interplay of classical and quantum dynamics in a thermal ensemble of atoms,” New J. Phys. 18, 053022 (2016).
[Crossref]

2015 (2)

T. R. Bromley, M. Cianciaruso, and G. Adesso, “Frozen quantum coherence,” Phys. Rev. Lett. 114, 210401 (2015).
[Crossref]

T. Zhong, J. M. Kindem, E. Miyazono, and A. Faraon, “Nanophotonic coherent light-matter interfaces based on rare-earth-doped crystals,” Nat. Commun. 6, 8206 (2015).
[Crossref]

2014 (4)

J. Hansom, C. H. H. Schulte, C. Le Gall, C. Matthiesen, E. Clarke, M. Hugues, J. M. Taylor, and M. Atatüre, “Environment-assisted quantum control of a solid-state spin via coherent dark states,” Nat. Phys. 10, 725–730 (2014).
[Crossref]

T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence,” Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
[Crossref]

B. Peng, S. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref]

2013 (3)

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111, 033601 (2013).
[Crossref]

Y. O. Dudin, L. Li, and A. Kuzmich, “Light storage on the time scale of a minute,” Phys. Rev. A 87, 031801 (2013).
[Crossref]

L. Giner, L. Veissier, B. Sparkes, A. S. Sheremet, A. Nicolas, O. S. Mishina, M. Scherman, S. Burks, I. Shomroni, D. V. Kupriyanov, P. K. Lam, E. Giacobino, and J. Laurat, “Experimental investigation of the transition between Autler-Townes splitting and electromagnetically-induced-transparency models,” Phys. Rev. A 87, 013823 (2013).
[Crossref]

2012 (2)

T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletic, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature 488, 57–60 (2012).
[Crossref]

F. De Martini and F. Sciarrino, “Colloquium: multiparticle quantum superpositions and the quantum-to-classical transition,” Rev. Mod. Phys. 84, 1765–1789 (2012).
[Crossref]

2011 (2)

A. Noguchi, Y. Eto, M. Ueda, and M. Kozuma, “Quantum-state tomography of a single nuclear spin qubit of an optically manipulated ytterbium atom,” Phys. Rev. A 84, 030301 (2011).
[Crossref]

P. M. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011).
[Crossref]

2010 (2)

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81, 041803 (2010).
[Crossref]

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[Crossref]

2009 (5)

H. Tanji, S. Ghosh, J. Simon, B. Bloom, and V. Vuletić, “Heralded single-magnon quantum memory for photon polarization states,” Phys. Rev. Lett. 103, 043601 (2009).
[Crossref]

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[Crossref]

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80, 023820 (2009).
[Crossref]

R. Zhao, Y. O. Dudin, S. D. Jenkins, C. J. Campbell, D. N. Matsukevich, T. A. B. Kennedy, and A. Kuzmich, “Long-lived quantum memory,” Nat. Phys. 5, 100–104 (2009).
[Crossref]

H. G. Barros, A. Stute, T. E. Northup, C. Russo, P. O. Schmidt, and R. Blatt, “Deterministic single-photon source from a single ion,” New J. Phys. 11, 103004 (2009).
[Crossref]

2008 (1)

K. S. Choi, H. Deng, J. Laurat, and H. J. Kimble, “Mapping photonic entanglement into and out of a quantum memory,” Nature 452, 67–71 (2008).
[Crossref]

2007 (4)

J. Simon, H. Tanji, S. Ghosh, and V. Vuletic, “Single-photon bus connecting spin-wave quantum memories,” Nat. Phys. 3, 765–769 (2007).
[Crossref]

N. Gisin, S. A. Moiseev, and C. Simon, “Storage and retrieval of time-bin qubits with photon-echo-based quantum memories,” Phys. Rev. A 76, 014302 (2007).
[Crossref]

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity,” Phys. Rev. A 76, 033835 (2007).
[Crossref]

D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[Crossref]

2006 (2)

M. V. Pack, R. M. Camacho, and J. C. Howell, “Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: theory,” Phys. Rev. A 74, 013812 (2006).
[Crossref]

D. N. Matsukevich, T. Chanelière, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, “Entanglement of remote atomic qubits,” Phys. Rev. Lett. 96, 030405 (2006).
[Crossref]

2005 (3)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[Crossref]

L. Yang, L. Zhang, X. Li, L. Han, G. Fu, N. B. Manson, D. Suter, and C. Wei, “Autler-Townes effect in a strongly driven electromagnetically induced transparency resonance,” Phys. Rev. A 72, 053801 (2005).
[Crossref]

2002 (2)

C. Y. Ye, A. S. Zibrov, Y. V. Rostovtsev, and M. O. Scully, “Unexpected Doppler-free resonance in generalized double dark states,” Phys. Rev. A 65, 043805 (2002).
[Crossref]

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, “Narrowing of electromagnetically induced transparency resonance in a Doppler-broadened medium,” Phys. Rev. A 66, 013805 (2002).
[Crossref]

2001 (2)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[Crossref]

G. S. Agarwal, T. N. Dey, and S. Menon, “Knob for changing light propagation from subluminal to superluminal,” Phys. Rev. A 64, 053809 (2001).
[Crossref]

2000 (2)

M. D. Lukin, S. F. Yelin, and M. Fleischhauer, “Entanglement of atomic ensembles by trapping correlated photon states,” Phys. Rev. Lett. 84, 4232–4235 (2000).
[Crossref]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[Crossref]

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[Crossref]

1995 (2)

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[Crossref]

Y.-Q. Li and M. Xiao, “Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms,” Phys. Rev. A 51, R2703–R2706 (1995).
[Crossref]

1991 (1)

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

1972 (1)

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–249 (1972).
[Crossref]

Adesso, G.

A. Streltsov, G. Adesso, and M. B. Plenio, “Colloquium: quantum coherence as a resource,” Rev. Mod. Phys. 89, 041003 (2017).
[Crossref]

T. R. Bromley, M. Cianciaruso, and G. Adesso, “Frozen quantum coherence,” Phys. Rev. Lett. 114, 210401 (2015).
[Crossref]

Agarwal, G. S.

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81, 041803 (2010).
[Crossref]

G. S. Agarwal, T. N. Dey, and S. Menon, “Knob for changing light propagation from subluminal to superluminal,” Phys. Rev. A 64, 053809 (2001).
[Crossref]

Álvarez, G. A.

D. Suter and G. A. Álvarez, “Colloquium: protecting quantum information against environmental noise,” Rev. Mod. Phys. 88, 041001 (2016).
[Crossref]

Anisimov, P. M.

P. M. Anisimov, J. P. Dowling, and B. C. Sanders, “Objectively discerning Autler-Townes splitting from electromagnetically induced transparency,” Phys. Rev. Lett. 107, 163604 (2011).
[Crossref]

Arndt, M.

M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
[Crossref]

Atatüre, M.

J. Hansom, C. H. H. Schulte, C. Le Gall, C. Matthiesen, E. Clarke, M. Hugues, J. M. Taylor, and M. Atatüre, “Environment-assisted quantum control of a solid-state spin via coherent dark states,” Nat. Phys. 10, 725–730 (2014).
[Crossref]

Barros, H. G.

H. G. Barros, A. Stute, T. E. Northup, C. Russo, P. O. Schmidt, and R. Blatt, “Deterministic single-photon source from a single ion,” New J. Phys. 11, 103004 (2009).
[Crossref]

Baumgratz, T.

T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence,” Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Bhaskar, M. K.

M. K. Bhaskar, D. D. Sukachev, A. Sipahigil, R. E. Evans, M. J. Burek, C. T. Nguyen, L. J. Rogers, P. Siyushev, M. H. Metsch, H. Park, F. Jelezko, M. Lončar, and M. D. Lukin, “Quantum nonlinear optics with a germanium-vacancy color center in a nanoscale diamond waveguide,” Phys. Rev. Lett. 118, 223603 (2017).
[Crossref]

Blatt, R.

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Supplementary Material (1)

NameDescription
» Supplement 1       Supplements

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Figures (4)

Fig. 1.
Fig. 1. (a) Effective three-level atomic system where states |1 and |2 are coupled to |3 by a continuous probe and a pulsed control field of Rabi frequencies (detunings): Ωp(Δp) and Ωc(Δc), respectively. Level |4 depicts additional states of neighboring ground-state manifold. Solid, horizontal arrows indicate co-propagating fields. (b) Experimental trace (dots) of EIT resonance with two-photon detuning (δ=ΔpΔc). Here, Iin, Itrans are the initial and transmitted probe intensities, respectively. Solid line is the Lorentz fit that corresponds to a line width of 34 kHz. (c) Schematic of experimental setup. ECDL, external cavity diode laser; Rb, rubidium vapor cell; P, probe (purple); C, control (red); R, repumper (dark yellow); Ram, Raman beam (green); AOM, acousto-optic modulator; Q, quarter-wave plate; H, half-wave plate; M, mirror; BS, 50:50 beam splitter; PBS, polarizing beam splitter; GT, Glan–Thompson polarizing beam cube; PD, photo detector; DSO, digital storage oscilloscope.
Fig. 2.
Fig. 2. (a) Evolution of the system in an effective Bloch-sphere corresponding to ground states |1 and |2 (see text). (b) Experimental trace (solid) of probe transmission, with a control field turned on (at t=0  μs) and off after 10 μs for an experimentally simulated, quasi-closed three-level system. Here, Δp=Δc=3.2γ3, Ωc=2.3×101γ3, and R=2.7×101γ3, where γ3=6.0(2π)  MHz is the radiative decay rate of |3. The level diagram in inset shows a counter-propagating repumper field (R) effectively closing the system. The dashed trace corresponds to numerical simulations. Frames (c) and (d) correspond to similar experimental and simulated traces for an open EIT system and an EIT configuration with counter-propagating fields. Ωc=2.3×101γ3 and 1.7×101γ3 for frames (c) and (d), respectively. Simulation parameters are chosen according to experiment.
Fig. 3.
Fig. 3. (a) EIT and Autler–Townes basis states in a Λ system. (b) Coherence quantifier C as a function of δ for varying control intensities. Near saturation intensity, the observed splitting in C is a signature of transition from EIT to ATS regime. Ωp=2.5×103γ3 and R=2.6×101γ3. Inset shows the steady-state probe transmission profile where any such signature is washed out due to power broadening. (c) Theoretically calculated coherence |ρ12ss| as a function of δ for varying control intensities. Here, Ωp=1.0×103γ3˜, 2Ωc=(I/2Isat)γ3˜, where γ3˜=1  MHz. (d) Experimentally measured C as a function of control intensity at δ=0. The red solid line is ΩpΩc/(Ωp2+Ωc2) fitting. Inset shows the variation of theoretically calculated |ρ12ss| with control intensity at δ=0. ID=IsatΓD/0.89γ3 is the saturation intensity for thermal atoms where ΓD=308  MHz (Supplement 1). Simulation parameters are chosen according to experiment.
Fig. 4.
Fig. 4. (a) Energy-level scheme for controlling coherence. Here, Ω and Ω+ are highly detuned Raman coherent fields with ϕR being the phase difference between them. Figure on the right shows the projection of Bloch vector in ρ12 plane for EIT and Raman field controlled coherence schemes, where ρ12EIT=ΩcΩp*/|Ωc|2 and ρ12R=iΩR*Γ3/|Ωc|2. Δϕ=(ϕcϕp)ϕR, where ϕp(c) is the phase of probe (control) field. (b) Sinusoidal variation of C as a function of ϕR. Circles and solid line show experimental and simulation results, respectively. Dashed (Cab) and dotted (Ccd) black lines indicate C at initial peak (region ab) and steady state (region cd) for EIT case. ΔC is the visibility of coherence, and ΔCo=CabCcd. ϕf corresponds to ϕR=120° (100° in simulation), at which C freezes to its initial maxima. (c) Experimental (solid) and simulated (dashed) time trace of probe transmission for EIT (red) and Raman field controlled coherence schemes at ϕf (blue). Here Ωc=2.5×101γ3, Ωp=3.5×103γ3, |Ω+|=|Ω|=3.7×101γ3, and ΔR=1.5ΓD. (d) ΔC as a function of ΔR with the dashed line showing 1/ΔR fit. Red dashed line indicates ΔCo for EIT system. Inset shows the simulations where Δρ12ss is the visibility in terms of ground-state coherence. Here, γex=γ3+γout as defined in Supplement 1.

Equations (5)

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

ρ13ss=[iΩc*ρ12ssiΩp*(ρ11ssρ33ss)]/Γ13,
C=|ρ13Ωcon,ssρ13Ωcoff,ss||ρ13Ωcoff,ss||Ωp||Ωc|,
C=h1h2h2|Ωp||Ωc|.
Cclosed>Copen>Cincoherent.
ρ12ss=ΩcΩp*|Ωc|2+iΩR*Γ3|Ωc|2,