Quantum fidelity of electromagnetically induced transparency: the full quantum theory.

We present a full quantum model to study the fidelity of single photons with different quantum states propagating in a medium exhibiting electromagnetically induced transparency (EIT). By using the general reservoir theory, we can calculate the quantum state of the transmitted probe photons that reveal the EIT phenomenon predicted by semiclassical theory while reflecting the influence of the quantum fluctuations of the strong coupling field. Our study shows that the coupling field fluctuations not only change the quantum state of the probe photons, but also slightly affect its transmittance. Moreover, we demonstrate that the squeezed coupling field can enhance the influence of its fluctuations on the quantum state of the probe photons, which means that the EIT effect can be manipulated by controlling the quantum state properties of the coupling field. The full quantum theory in this paper is suitable for studying quantum systems related to the EIT mechanism that would allow us to examine various quantum effects in EIT-based systems from a full quantum perspective.

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.

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.

High-efficiency backward four-wave mixing by quantum interference.

Electromagnetically-induced-transparency-based four-wave mixing (FWM) in a resonant four-level double-Λ system has a maximum conversion efficiency (CE) of 25% due to spontaneous emission. Herein, we demonstrate that spontaneous emission can be considerably suppressed by arranging the applied laser beams in a backward configuration. With the backward double-Λ FWM scheme, we observe a CE of 63% in cold rubidium atoms with an optical depth (OD) of 48. To the best of our knowledge, this is the first observation of a CE exceeding the conversion limit in resonant FWM processes. Furthermore, we present a theoretical model that includes the phase-mismatch effect in the backward double-Λ FWM system. According to the theoretical model, the present scheme can achieve 96% CE using a medium with a large OD of 200 under ideal conditions. Such an efficient frequency conversion scheme has potential applications in optical quantum information technology.

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.

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.

Femtowatt-light-level phase measurement of slow light pulses via beat-note interferometer.

We report on an experimental demonstration of applying the beat-note interferometer to simultaneously measure the phase and amplitude variations of light pulses after propagating through an electromagnetically induced transparency medium at femtowatt-light levels. Furthermore, we observe that the measured phase noise approaches the shot-noise level arising from the fluctuations of detected photons.

Manipulating the retrieved frequency and polarization of stored light pulses.

We have experimentally demonstrated that stored and retrieved light pulses have different frequencies but maintain phase coherence; a stored light pulse is released with a different polarization. However, the manipulation process causes an energy loss of the retrieved pulse. We have discovered that Clebsch-Gordan coefficients among the Zeeman sublevels play an important role in the energy loss and have demonstrated a solution for avoiding the energy loss.

Low-light-level all-optical switching.

We propose an all-optical switch that utilizes the technique of storage and retrieval of light pulses. A single photon (probe pulse) switched by another (switching pulse) is feasible, and the on-off ratio can be as large as 10 dB. We have experimentally demonstrated that the energy of the retrieved probe pulse is reduced to about 10% because of the presence of a switching pulse with an energy per unit area of one photon per lambda(2)/(2pi). The achieved result does not depend on the coupling intensity, the atomic optical density, or the width and shape of the switching pulse.

Low-light-level cross-phase-modulation based on stored light pulses.

We experimentally demonstrate a low-light-level cross-phase-modulation (XPM) scheme based on the light-storage technique in laser-cooled 87Rb atoms. The proposed scheme can achieve a similar phase shift and has the same figure of merit as one using static electromagnetically induced transparency under the constant coupling field. Nevertheless, the phase shift and the energy loss of a probe pulse induced by a signal pulse are neither influenced by the coupling intensity nor by the atomic optical density in the light-storage XPM scheme. This scheme enhances the flexibility of the experiment and makes possible conditional phase shifts on the order of pi with single photons.

Low-light-level photon switching by quantum interference.

We report an experimental demonstration of low-light-level photon switching by quantum interference in laser-cooled 87Rb atoms. A resonant probe pulse with an energy per unit area of one photon per lambda2/2pi propagates through the optically thick atoms. Its energy transmittance is greater than 63%, or a loss of less than e(-1), because of the effect of electromagnetically induced transparency. In the presence of a switching pulse with an energy per unit area of 1.4 photons per lambda2/2pi, the energy transmittance of the same probe pulse becomes less than 37%, or e(-1). This substantial reduction of probe transmittance caused by switching photons may lead to potential applications in single-photon-level nonlinear optics and manipulation of quantum information.