1. Introduction

Photon pair sources are an important resource for a large number of quantum optics experiments; in particular, entangled two-photon states have been used to confirm the foundations of quantum mechanics and constitute today one of the building blocks of quantum information and communication [1]. The most widely used way to produce entangled photon pairs is spontaneous parametric down-conversion (SPDC), in which one pump photon is annihilated into two photons sharing its energy which can be entangled in one or more of their degrees of freedom: frequency, polarization, momentum, and orbital angular momentum [2]. In terms of frequency, a narrow band pump beam produces anti-correlated twin photons. Recent developments in quantum information theory have arisen a growing interest on ‘generalized’ states of frequency correlation [3]. Two related sample applications are given by optical quantum computation protocols based on indistinguishable (and thus uncorrelated) photons [4], and the improvement of clock synchronization based on frequency correlated photons [5]. In this context, counterpropagating phase matching, in which a pump field impinges on top of a waveguide generating two counter-propagating wave-guided signal and idler beams, has been demonstrated to be a flexible and versatile means to generate generalized states of frequency correlation [6].

In addition, a great deal of effort has been devoted to the miniaturization of quantum information technology on semiconductor chips, including micro-traps for ions [7, 8] and atoms [9], and quantum-dot based sources of entangled photons [10, 11]. Compared with the last approach, parametric generation in semiconductor waveguides has the advantage of room-temperature operation and a highly directional emission, which dramatically enhances the collection efficiency.

In this work we present a semiconductor ridge microcavity source of quantum light that combines the potential of a full optoelectronic integration with the versatility of two photon state generation under counterpropagating phase matching. In the following, we will first describe the working principle and the design of the device. We then present the SPDC characterisation of the source (Section 3) and a Hong-Ou-Mandel experiment aimed at demonstrating the indistinguishability between the two photons of the pair and to evaluate the potentiality of entanglement (Section 4). Finally, we will conclude with the perspectives opened by these results (Section 5).

 

Fig. 1. Parametric generation of counterpropagating twin photons in a multilayer waveguide. (a) Counterpropagating phase-matching scheme. The phase matching is automatically obtained in the z direction; QPM is provided by a periodic modulation of the nonlinear susceptibility in the waveguide core along the epitaxial direction. (b) Amplitude of the interacting modes and optical index profile of the microcavity. The pump field enhancement strongly improves the generation efficiency.

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2. Working principle and design of the semiconductor ridge microcavity

A preliminary demonstration of a twin-photon semiconductor waveguide source based on counterpropagating phase-matching has been reported in an AlGaAs waveguide [12, 13]. In that experiment [Fig. 1(a)], a pump field impinges on top of the waveguide generating two counter-propagating, orthogonally polarized wave-guided twin photons through SPDC.

The frequencies of the emitted fields are fixed by the energy (ω_p = ω_s+ω_i) and momentum (k_p sinθ = n_sk_s - n_ik_i) conservation, where ω_p, ω_s and ω_i (k_p, k_s and k_i) are the frequencies (wave vectors) of pump, signal and idler; θ is the angle of incidence of the pump beam, and n_s and n_i are the effective indices of the signal and idler modes. Momentum conservation in the epitaxial direction is fulfilled by alternating Al _0.25 Ga _0.75 As/Al _0.80 Ga _0.20 As layers having different nonlinear susceptibilities to implement a Quasi Phase Matching (QPM) scheme. Since for each value of λ and θ there is always a pair of photons satisfying these conservation laws, this geometry is also said to be auto-phase-matched [14]. Moreover, as the three interacting fields propagate in different directions, there is no need to filter the pump beam from the down-converted TE-TM fields and to separate these at a beam splitter, which represents an advantage with respect to collinear configurations. However, the performances reported in Ref. [12] were affected by low conversion efficiency and low signal/noise ratio due to photo-luminescence from the substrate, which prevented the utilization of that source for quantum optics experiments.

In the completely new design reported here, we included two Distributed Bragg Reflectors (DBRs), one on the top and the other at the bottom of the waveguide, in order to create a microcavity for the pump beam and obtain a nearly standing wave therein [Fig. 1(a)]. In this configuration, the internal amplitude of the pump field is much greater than outside; moreover, the high reflectivity of the lower DBR reduces the penetration of the pump field into the substrate, thus limiting the photo-luminescence noise [15]. Such vertical microcavity, designed with the transfer matrix method, consists of : air/ DBR up (18-period asymmetrical Al _0.35 Ga _0.65 As/Al _0.90 Ga _0.10 As) / QPM (4.5 period Al _0.25 Ga _0.75 As/Al _0.80 Ga _0.20 As)/ DBR down (41-period asymmetrical Al _0.35 Ga _0.65 As/Al _0.90 Ga _0.10 As)/ substrate (GaAs). The DBRs placed on both sides of the QPM region, play a double role: (1) waveguide cladding for the counter-propagating signal and idler; (2) mirror for the vertical cavity resonating at the pump wavelength. The sample was first grown by molecular beam epitaxy on a (100) GaAs substrate, then chemically etched to create 2.5 – 3.5 μm deep ridges with 5 – 6 μm widths. The efficiency enhancement factor allowed by the vertical microcavity can be expressed as [15]:

where η_cavity (η ₀) is the conversion efficiency defined as the ratio between the number of generated pairs and the number of pump photons, in the presence (absence) of the microcavity; n is the mean effective index of the waveguide, T_up (T_down) the transmission coefficients of the upper (lower) mirror, and F the finesse of the cavity. In order to have an efficient process in the whole device, the resonance wavelength of the vertical microcavity must be the same over the entire length of the ridge; for this reason, in our design the upper value of F is set by the homogeneity of the sample, i.e. by the epitaxial growth (in our case F ~ 100). Figure 1(b) shows the calculated amplitude profiles of the interacting fields, at cavity resonance.

3. SPDC measurements

In our geometry, two equally probable interactions occur: in the former (interaction 1), the guided mode copropagating with the z component of the pump beam (signal mode) is TE polarized and the counterpropagating one (idler mode) is TM polarized; in the latter (interaction 2), the reverse occurs. Since the signal and idler central frequencies are determined by the conservation of energy and momentum in the z direction, the incidence angle of the pump beam provides a very convenient means to tune them. The X-shaped tunability curves of our source, typical of type II interactions, are shown in Fig. 2(a). The degeneracy angles of interactions 1 and 2 are different from zero due to the modal birefringence of the waveguide; the geometry imposes that they are symetrical with respect to θ = 0°. Note that a crucial feature of this device is the possibility of directly generating Bell states by simultaneously pumping at the two degeneracy angles.

Figure 2(b) shows the SPDC spectrum obtained with a TE polarized pump beam provided by a pulsed Ti:Sapphire laser (100 ns pulses, 3 kHz repetition rate), with wavelength λ_p = 759.5 nm and linewidth 0.3 nm. The beam is collimated with a cylindrical lens on top of the waveguide ridge. The generated photons are collected from either facet of the waveguide with a microscope objective, spectrally analyzed with a monochromator, and then coupled into a fibered InGaAs single-photon avalanche photodiode (Id 201 from ID Quantique) with 50 ns gate and 15 % detection efficiency. The spectra confirm the occurrence of the two processes predicted in Fig. 2(a) and demonstrate the possibility of direct generation of polarization-entangled states. The amplitude difference between the observed signal and idler is due to the fact that on path R the idler photons are collected after their reflection on the left facet, while on path L the signal photons are collected after their reflection on the right facet. An antireflection coating on both facets of the sample would allow an automatic separation of the photons of each pair and their direct coupling into two optical fibers, through standard pigtailing. In this experiment, the bandwidth of the generated photons stems from the convolution of the pump spectrum (0.3 nm FWHM), the phase matching band (0.3 nm FWHM for a sample of length L = 1 mm) and of the monochromator resolution (0.1 nm). In the case of a monochromatic pump beam, the spectrum of the down-converted photons is given by the usual function sinc ²(∆kL/2). One of the main advantages of the counterpropagating geometry arises from the rapid increase of ∆k when one moves away from perfect phase matching, which leads to a bandwidth of the downconverted photons that is one to two orders of magnitude narrower than for collinear geometries: this lends itself to long-distance propagation in optical fibers, with a negligible chromatic dispersion. Measuring the amount of detected photons, we estimate the brightness of our twin photon source to be around 10^-11 pairs/pump photons, representing an enhancement of at least two orders of magnitude with respect to the device presented in Ref. [12]. The consequent improvement of the signal/noise ratio makes the source suitable for quantum optics applications.

4. Hong-Ou-Mandel (HOM) interference measurements

Since polarization-entangled photon pairs require the indistinguishability of the two photons for any degree of freedom but polarization, a HOM experiment [16] is perfectly suited to measure the distinguishability of two individual photons, thus giving an estimate of the entanglement quality [20, 21]. In this type of experiment, two indistinguishable photons enter a 50/50 beam splitter at the same time; the destructive interference makes them exit the device through the same output, thus inducing a dip in the coincidence histogram. The visibility of this dip gives informations on the quality of indistinguishability and thus on the potential amount of entanglement, while its width corresponds to the coherence length of the interfering photons. The application of this test to our source requires that the two photons of the pair are made indistinguishable by rotating the polarization of one of them by 90°. Figure 3(a) shows the experimental layout for the two-photon interference. The waveguide is pumped with the Ti:Sapphire laser described in the previous section, over a length of 0.65 mm, with a peak power of 1.5 W, and an angle of incidence θ_deg = 0.37°, corresponding to the degeneracy angle of interaction 1. This leads to the generation of 10 pairs per pump pulse, equally distributed on the two kinds of interactions; the pairs generated via interaction 1 are selected with two polarizers. A retroreflector placed in one arm of the interferometer is used to adjust the relative delay between the two photons and a half-wave plate is used to make their polarizations parallel. The photons recombine onto a fibered 50/50 beam splitter and the signal emerging from its two outputs is detected. A time-interval analyzer records the delay between the arrival times of the generated photons. The overall transmission coefficient of the interferometer is 12.5 % (70 % waveguide facets, 70 % microscope objectives, 50 % interference filters, 50 % fiber beam splitter). The interference filters, centred at 1520 nm with a bandwidth of 10 nm, are used to reduce the luminescence noise (which is a white noise of the order of 0.05 photons per nanometre per pump pulse, over a width of a few hundred nanometres). The photons are detected via two InGaAs single-photon avalanche photodiodes; in our operating conditions their detection rate is 3kHz, their gate is 100 ns, their detection efficiency is 20 % and the dark-count rate is 20 counts/s. This set-up typically allows to detect a signal of 400 counts/s, with a luminescence noise of about 20 counts/s.

 

Fig. 2. Tunability curves and emission spectra. (a) Line: Calculated tuning curves as a function of the pump incident angle for a pump wavelength of 760nm and the structure described in the text. Dashed lines show the selected incident angles for the experiments. (b) SPDC spectra for an angle of incidence of θ ₁ = 3.1° in the photon-counting regime. The peaks correspond to the four kinds of photons that can be generated via the two possible interactions. The background noise here is due to the dark counts of the detectors. Path R(L) denote the detection path of photons exiting the right (left) facet.

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Figure 3(b) reports the dip observed in the coincidence counts vs the optical path length difference between the two arms, once the accidental counts have been removed: this dip is a clear signature of the destructive interference between the two photons. The solid line shows the fit between our data and the theoretical expression of the HOM dip [17, 18]:

 

Fig. 3. Two-photon interference set-up and HOM dip. (a) Sketch of the experimental setup used for the two photon interference. The two photons generated in the selected interaction are combined in a fibered 50/50 coupler, where quantum interference occurs. The polarization of one of the two photons is rotated of 90° with a half-wave plate. A retroreflector placed in one arm of the interferometer is used to adjust the relative delay of the two photons. (b) Coincidence counts in 3 min (total counts - accidental counts) as a function of the relative length of the two arms. The accidental coincidence counts accounts for 14 % of the total coincidence counts outside the dip. The coincidence windows taken into account is 400 ps. The error bars are determined by the Poisson distribution (the square-root sum of the total coincidence counts) and the solid line is the numerical fit.

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where N_c is the normalized coincidence rate, V the visibility, ∆z is the optical path difference, λ is the degeneracy wavelength, and ∆λ is the full width at half maximum spectral intensity. The two fitting parameters are ∆λ and V; for the first one we obtain 0.53 nm, in excellent agreement with the theoretical value 0.52 nm ± 0.04 nm expected for the sample length L = 0.65 mm [19], while for the second one we obtain 85 %. We emphasize that this value is obtained without using any filters, as is often done in order to reduce the spectral bandwidth of the emitted photons. The main cause of the less-than-perfect visibility in our experiment is due to the fact that the waveguide facets are not anti-reflection coated and have reflectivity coefficients for TE and TM modes R_TE = 27% and R_TM = 25% respectively. Note that, in our set up, a coincidence event can be not only due to two photons directly transmitted by the facets, but also to one photon directly transmitted and one photon having experienced two reflections before leaving the waveguide. Since in the latter case, the path difference for the two photons is not the same as for the former case, these photons do not contribute to the dip. These events should give rise to satellite dips 6 mm away from the main dip, which are not visible in our measurements do the uncertainties affecting our data. Coincidence events may also be due to photons from interaction 2 (which are partially transmitted by the 10 nm interference filters) having experienced one reflection each. These photons are not degenerate so they do not contribute to the dip either. If we consider the first case to have a probability 1, the second case has a probability R ² _TE+R _{2 TM} and the third case has a probability (T _inter2/T _inter1)² R_TER_TM, where T _inter1(2) is the transmission coefficient of the interferential filter for interaction 1(2). The visibility is then given by V = 1/(1 +R ² _TE +R ² _TM +(T _inter2/T _inter1)² R_TER_TM) = 86%±1 %, which is in agreement with our experimental results.

5. Conclusion

The above results constitute the first demonstration of two-photon interference obtained with a semiconductor integrated source at room temperature. They pave the way to the demonstration of a few interesting features associated to the counterpropagating geometry, such as the direct generation of polarization-entangled Bell states or the two-photon state controlled generation via the proper choice of the spatial and spectral pump beam profile [3, 6, 22]. The efficiency of this device, along with the high-quality quantum properties of the generated photons and their telecom wavelength, makes this source a serious candidate for integrated quantum photonics.