Universal relation between the conditional auto-correlation function and the cross-correlation function of biphotons.

We systematically studied the relation between the conditional auto-correlation function (CACF) and cross-correlation function (CCF) of biphotons or pairs of single photons. The biphotons were generated from a heated atomic vapor via the spontaneous four-wave mixing (SFWM) process. In practical usage, one single photon of a pair is utilized as the heralding photon, and another is employed as the heralded photon. Motivated by the data of CACF of the heralded photons versus CCF, we proposed a universal formula to predict the CACF. The derived formula was based on general theory and is also valid for the biphoton generation process of spontaneous parametric down-conversion (SPDC). With the formula, we utilized the experimentally determined parameters to predict CACFs, which can well agree with the measured CACFs. The proposed formula enables one to quantitatively know the CACF of heralded single photons without the measurement of Hanbury-Brown-Twiss-type three-fold coincidence count. This study provides a better understanding of biphoton generation using the SFWM or SPDC process. Our work demonstrates a valuable tool for analyzing a vital property of how the heralded photons are close to Fock-state single photons.

Experimental Demonstration of Stationary Dark-State Polaritons Dressed by Dipole-Dipole Interaction.

Dark-state polaritons (DSPs) based on the effect of electromagnetically induced transparency are bosonic quasiparticles, representing the superpositions of photons and atomic ground-state coherences. It has been proposed that stationary DSPs are governed by the equation of motion closely similar to the Schrödinger equation and can be employed to achieve Bose-Einstein condensation (BEC) with transition temperature orders of magnitude higher than that of the atomic BEC. The stationary-DSP BEC is a three-dimensional system and has a far longer lifetime than the exciton-polariton BEC. In this Letter, we experimentally demonstrated the stationary DSP dressed by the Rydberg-state dipole-dipole interaction (DDI). The DDI-induced phase shift of the stationary DSP was systematically studied. Notably, the experimental data are consistent with the theoretical predictions. The phase shift can be viewed as a consequence of elastic collisions. In terms of thermalization to achieve BEC, the µm^{2}-size interaction cross section of the DDI can produce a sufficient elastic collision rate for the stationary DSPs. This Letter makes a substantial advancement toward the realization of the stationary-DSP BEC.

Optical-density enhanced quantum entanglement via four-wave mixing process.

We theoretically propose a scheme to generate a strong continuous-variable quantum entangled light source in four-wave mixing (FWM) process by increasing the optical density of atomic medium. By properly choosing the input coupling field Rabi frequency and detuning, the optimized entanglement can be achieved to be better than -17 dB at an optical density of approximately 1, 000, which has been realized in atomic media. Besides, with the optimized one-photon detuning and coupling Rabi frequency, the optimum entanglement degree can be greatly enhanced with the increment of optical density. We also examine the effects of atomic decoherence rate and two-photon detuning on entanglement in a realistic setting, and evaluate the experimental feasibility. We find that the entanglement can be further improved by considering two-photon detuning. In addition, with optimum parameters the entanglement is robust against the decoherence. The strong entanglement provides a promising applications in continuous-variable quantum communications.

Generation of quantum entanglement based on electromagnetically induced transparency media.

Quantum entanglement is an essential ingredient for the absolute security of quantum communication. Generation of continuous-variable entanglement or two-mode squeezing between light fields based on the effect of electromagnetically induced transparency (EIT) has been systematically investigated in this work. Here, we propose a new scheme to enhance the degree of entanglement between probe and coupling fields of coherent-state light by introducing a two-photon detuning in the EIT system. This proposed scheme is more efficient than the conventional one, utilizing the ground-state relaxation (population decay or dephasing) rate to produce entanglement or two-mode squeezing which adds far more excess fluctuation or noise to the system. In addition, maximum degree of entanglement at a given optical depth can be achieved with a wide range of the coupling Rabi frequency and the two-photon detuning, showing our scheme is robust and flexible. It is also interesting to note that while EIT is the effect in the perturbation limit, i.e. the probe field being much weaker than the coupling field and treated as a perturbation, there exists an optimum ratio of the probe to coupling intensities to achieve the maximum entanglement. Our proposed scheme can advance the continuous-variable-based quantum technology and may lead to applications in quantum communication utilizing squeezed light.

Generation of sub-MHz and spectrally-bright biphotons from hot atomic vapors with a phase mismatch-free scheme.

We utilized the all-copropagating scheme, which maintains the phase-match condition, in the spontaneous four-wave mixing (SFWM) process to generate biphotons from a hot atomic vapor. The linewidth and spectral brightness of our biphotons surpass those of the biphotons produced with the hot-atom SFWM in the previous works. Moreover, the generation rate of the sub-MHz biphoton source in this work can also compete with those of the sub-MHz biphoton sources of the cold-atom SFWM or cavity-assisted spontaneous parametric down conversion. Here, the biphoton linewidth is tunable for an order of magnitude. As we tuned the linewidth to 610 kHz, the generation rate per linewidth is 1,500 pairs/(s·MHz) and the maximum two-photon correlation function, gs,as(2), of the biphotons is 42. This gs,as(2) violates the Cauchy-Schwarz inequality for classical light by 440 folds, and demonstrates that the biphotons have a high purity. By increasing the pump power by 16 folds, we further enhanced the generation rate per linewidth to 2.3×104 pairs/(s·MHz), while the maximum gs,as(2) became 6.7. In addition, we are able to tune the linewidth down to 290±20 kHz. This is the narrowest linewidth to date among all single-mode biphoton sources of room-temperature and hot media.

Efficient frequency conversion based on resonant four-wave mixing.

Efficient frequency conversion of photons has important applications in optical quantum technology because the frequency range suitable for photon manipulation and communication usually varies widely. Recently, an efficient frequency conversion system using a double-Λ four-wave mixing (FWM) process based on electromagnetically induced transparency (EIT) has attracted considerable attention because of its potential to achieve a nearly 100% conversion efficiency (CE). To obtain such a high CE, the spontaneous emission loss in this resonant-type FWM system must be suppressed considerably. A simple solution is to arrange the applied laser fields in a backward configuration. However, the phase mismatch due to this configuration can cause a significant decrease in CE. Here, we demonstrate that the phase mismatch can be effectively compensated by introducing the phase shift obtained by two-photon detuning. Under optimal conditions, we observe a wavelength conversion from 780 to 795 nm with a maximum CE of 91.2%±0.6% by using this backward FWM system at an optical depth of 130 in cold 87Rb atoms. The current work represents an important step toward achieving low-loss, high-fidelity quantum frequency conversion based on EIT.

Mean field theory of weakly-interacting Rydberg polaritons in the EIT system based on the nearest-neighbor distribution.

The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weakly-interacting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt with the strongly-interacting cases. Here, we consider the weakly-interacting regime and develop a mean field model based on the nearest-neighbor distribution. Using the mean field model, we further derive the analytical formulas for the attenuation coefficient and phase shift of the output probe field. The predictions from the formulas are consistent with the experimental data in the weakly-interacting regime, verifying the validity of our model. As the DDI-induced phase shift and attenuation can be seen as the consequences of elastic and inelastic collisions among particles, this work provides a very useful tool for conceiving ideas relevant to the EIT system of weakly-interacting Rydberg polaritons and for evaluating experimental feasibility.

Ultranarrow-bandwidth filter based on a thermal EIT medium.

We present high-contrast electromagnetically-induced-transparency (EIT) spectra in a heated vapor cell of single isotope 87Rb atoms. The EIT spectrum has both high resonant transmission up to 67% and narrow linewidth of 1.1 MHz. We get rid of the possible amplification resulted from the effects of amplification without population inversion and four-wave mixing. Therefore, this high transmitted light is not artificial. The theoretical prediction of the probe transmission agrees well with the data and the experimental parameters can be derived reasonably from the model. Such narrow and high-contrast spectral profile can be employed as a high precision bandpass filter, which provides a significant advantage in terms of stability and tunability. The central frequency tuning range of the filter is larger than 100 MHz with out-of-band blocking ≥15 dB. This bandpass filter can effectively produce light fields with subnatural linewidth. Nonlinearity associating with the narrow-linewidth and high-contrast EIT profile can be very useful in the applications utilizing the EIT effect.

Highly Efficient Coherent Optical Memory Based on Electromagnetically Induced Transparency.

Quantum memory is an important component in the long-distance quantum communication based on the quantum repeater protocol. To outperform the direct transmission of photons with quantum repeaters, it is crucial to develop quantum memories with high fidelity, high efficiency and a long storage time. Here, we achieve a storage efficiency of 92.0 (1.5)% for a coherent optical memory based on the electromagnetically induced transparency scheme in optically dense cold atomic media. We also obtain a useful time-bandwidth product of 1200, considering only storage where the retrieval efficiency remains above 50%. Both are the best record to date in all kinds of schemes for the realization of optical memory. Our work significantly advances the pursuit of a high-performance optical memory and should have important applications in quantum information science.

Enhanced spectral profile in the study of Doppler-broadened Rydberg ensembles.

Combination of the electromagnetically-induced-transparency (EIT) effect and Rydberg-state atoms has attracted great attention recently due to its potential application in the photon-photon interaction or qubit operation. In this work, we studied the Rydberg-EIT spectra with room-temperature 87Rb atoms. Spectroscopic data under various experimental parameters all showed that the contrast of EIT transparency as a function of the probe field intensity is initially enhanced, reaches a maximum value and then decays gradually. The contrast of spectral profile at the optimum probe field intensity is enhanced by 2-4 times as compared with that at weakest intensity. Moreover, the signal-to-noise ratio of the spectrum can potentially be improved by 1 to 2 orders of magnitude. We provided a theoretical model to explain this behavior and clarified its underlying mechanism. Our work overcomes the obstacle of weak signal in the Rydberg-EIT spectrum caused by an apparent relaxation rate of the Rydberg polariton and weak coupling transition strength, and provides the useful knowledge for the Rydberg-EIT study.

Large Cross-Phase Modulations at the Few-Photon Level.

We demonstrate an efficient cross-phase modulation (XPM) based on a closed-loop double-Λ system. The property of the double-Λ medium can be controlled by changing the phases of the applied optical fields. This phase-dependent XPM scheme can achieve large phase modulations at low-light intensities without requiring cavities or tightly focusing laser beams. With this scheme, we observe a π-level phase shift with two pulses, both consisting of eight photons in cold rubidium atoms. Such a novel scheme provides a simple route to generate strong interactions between photons and may have potential applications in all-optical quantum signal processing.

High conversion efficiency in resonant four-wave mixing processes.

We propose a new scheme of the resonant four-wave mixing (FWM) for the frequency up or down conversion, which is more efficient than the commonly-used scheme of the non-resonant FWM. In this new scheme, two control fields are spatially varied such that a probe field at the input can be converted to a signal field at the output. The efficiency of probe-to-signal energy conversion can be 90% at medium's optical depth of about 100. Our proposed scheme works for both the continuous-wave and pulse cases, and is flexible in choosing the control field intensity. This work provides a very useful tool in the nonlinear frequency conversion.

Experimental demonstration of spinor slow light.

Slow light based on the effect of electromagnetically induced transparency is of great interest due to its applications in low-light-level nonlinear optics and quantum information manipulation. The previous experiments all dealt with the single-component slow light. Here, we report the experimental demonstration of two-component or spinor slow light using a double-tripod atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by six light fields. The oscillation due to the interaction between the two components was observed. On the basis of the stored light, our data showed that the double-tripod scheme behaves like the two outcomes of an interferometer enabling precision measurements of frequency detuning. We experimentally demonstrated a possible application of the double-tripod scheme as quantum memory/rotator for the two-colour qubit. Our study also suggests that the spinor slow light is a better method than a widely used scheme in the nonlinear frequency conversion.

Coherence properties of amplified slow light by four-wave mixing.

We present an experimental study of the coherence properties of amplified slow light by four-wave mixing (FWM) in a three-level electromagnetically induced transparency (EIT) system driven by one additional pump field. High energy gain (up to 19) is obtained with a weak pump field (a few mW/cm2) using optically dense cold atomic gases. A large fraction of the amplified light is found to be phase incoherent to the input signal field. The dependence of the incoherent fraction on pump field intensity and detuning and the control field intensity is systematically studied. With the classical input pulses, our results support a recent theoretical study by Lauk et al. [Phys. Rev. A88, 013823 (2013)], showing that the noise resulting from the atomic dipole fluctuations associated with spontaneous decay is significant in the high gain regime. This effect has to be taken into consideration in EIT-based applications in the presence of FWM.

Coherent optical memory with high storage efficiency and large fractional delay.

A high-storage efficiency and long-lived quantum memory for photons is an essential component in long-distance quantum communication and optical quantum computation. Here, we report a 78% storage efficiency of light pulses in a cold atomic medium based on the effect of electromagnetically induced transparency. At 50% storage efficiency, we obtain a fractional delay of 74, which is the best up-to-date record. The classical fidelity of the recalled pulse is better than 90% and nearly independent of the storage time, as confirmed by the direct measurement of phase evolution of the output light pulse with a beat-note interferometer. Such excellent phase coherence between the stored and recalled light pulses suggests that the current result may be readily applied to single photon wave packets. Our work significantly advances the technology of electromagnetically induced transparency-based optical memory and may find practical applications in long-distance quantum communication and optical quantum computation.

Demonstration of the interaction between two stopped light pulses.

This study reports the first experimental demonstration that two light pulses were made motionless and interacted with each other through a medium. The scheme with motionless light pulses maximizes the interaction time and can achieve a considerable efficiency even below single-photon level. To demonstrate the enhancement of optical nonlinear efficiency, the experiment in this study used the process of one optical pulse switched by another based on the effect of electromagnetically induced transparency. Moving light pulses activate switching at an energy per area of 2 photons per atomic absorption cross section as discussed in [Phys. Rev. Lett. 82, 4611 (1999)]. This study demonstrates that motionless light pulses can activate switching at 0.56 photons per atomic absorption cross section, and that the light level can be further reduced by increasing the optical density of the medium. The result of this work enters a new regime of low-light physics.

EIT-based all-optical switching and cross-phase modulation under the influence of four-wave mixing.

All-optical switching (AOS) or cross-phase modulation (XPM) based on the effect of electromagnetically induced transparency (EIT) makes one photon switched or phase-modulated by another possible. The existence of four-wave mixing (FWM) process greatly diminishes the switching or phase-modulation efficiency and hinders the single-photon operation. We proposed and experimentally demonstrated an idea that with an optimum detuning the EIT-based AOS can be completely intact even under the influence of FWM. The results of the work can be directly applied to the EIT-based XPM. Our work makes the AOS and XPM schemes more flexible and the single-photon operation possible in FWM-allowed systems.

Hiding single photons with spread spectrum technology.

We describe a proof-of-principal experiment demonstrating the use of spread spectrum technology at the single photon level. We show how single photons with a prescribed temporal shape, in the presence of interfering noise, may be hidden and recovered.

Observation of phase variation within stationary light pulses inside a cold atomic medium.

The successful formation of stationary light pulses in a cold atomic medium was demonstrated recently. However, unlike in hot media, a detuning between the counterpropagating fields had to be applied. Here we demonstrate that a significant nonuniform phase variation can be induced during a period of stationary light owing to off-resonantly driven transitions. The experimental results are in good agreement with theoretical predictions for media of low optical depth. For media of high optical depth the numerical simulations indicate that such phase variation becomes negligible. Thus stationary light based on this coupling scheme could be used for possible future applications in quantum information processing.

Stationary light pulses in cold atomic media and without Bragg gratings.

We study the creation of stationary light pulses (SLPs), i.e., light pulses without motion, based on the effect of electromagnetically induced transparency with two counterpropagating coupling fields in cold atoms. We show that the Raman excitations created by counterpropagating probe and coupling fields prohibit the formation of SLPs in media of cold and stationary atoms such as laser-cooled atom clouds, Bose condensates or color-center crystals. A method is experimentally demonstrated to suppress these Raman excitations and SLPs are realized in laser-cooled atoms. Furthermore, we report the first experimental observation of a bichromatic SLP at wavelengths for which no Bragg grating can be established. Our work advances the understanding of SLPs and opens a new avenue to SLP studies for few-photon nonlinear interactions.