Non-adiabatic resonant transient response in electromagnetically induced transparency of hot rubidium atoms with a buffer gas background

Using electromagnetically induced transparency (EIT), it is possible to delay and store light in atomic ensembles. Theoretical modeling and recent experiments have suggested that the EIT storage mechanism can be used as a memory for quantum information. We present experiments that quantify the noise performance of an EIT system for conjugate amplitude and phase quadratures. It is shown that our EIT system adds excess noise to the delayed light that has not hitherto been predicted by published theoretical modeling. In analogy with other continuous-variable quantum information systems, the performance of our EIT system is characterized in terms of conditional variance and signal transfer.

We review our work on electromagnetically induced transparency (EIT) as a potentially key enabling science for few-qubit Quantum Information Technology (QIT). EIT systems capable of providing two-qubit phase shifts as large as pi are possible in a condensed matter system such as NV-diamond, but the potentially large residual absorption necessarily arising under this condition significantly reduces the fidelity of a nonlinear optical gate based on EIT. Instead, we emphasize that a universal set of quantum gates can be constructed using EIT systems that provide cumulative phase shifts (and residual absorptions) that are much smaller than unity. We describe a single-photon quantum nondemolition detector and a two-photon parity gate as basic elements of a nonlinear optical quantum information processing system.

Optical quantum memory plays an important role in scaling-up linear optical quantum computations and longdistance quantum communication. For effectively realizing such tasks, a long-lived and highly-efficient quantum memory is needed. The dynamic electromagnetically-induced-transparency (EIT) process can be used for completing an absorptive storage scheme in an atomic ensemble. In such a process, the quantum states of coming single photons can be coherently transformed into spin waves associated with coherences between atomic ground levels via switching off controlling light beam. For storing a single-mode optical signal, a pair of ground levels is involved. While for storing an optical polarization qubit, i.e., two orthogonal polarization modes, the coherence between two pairs of ground levels will be involved. Also, to obtain a high efficiency in the EIT optical storage, the optical-depth of the cold ensemble should be high. For prolonging the coherent time of the spin waves stored in atomic ensemble, decoherence between spin waves due to atomic motion and non-uniform Zeeman shift of ground levels should be effectively suppressed. Recently, a long-lived and highly-efficient optical quantum memory for single-mode storage in a high-optical-depth cold atom ensemble has been experimentally demonstrated via the gradient echo memory scheme (2016 Optical 3 100). While, for the optical polarization qubit storage, a long lifetime (in ms) and high-fidelity EIT storage experiment has been achieved by our group, but the storage efficiency in the experiment is very low (8%) due to lower optical depth of the cold ensemble (2013 Phys. Rev. Lett. 111 240503). The storage efficiency in long-lived storage of two orthogonal polarization modes still needs further improving. Here in this paper we demonstrate an experiment of long-lived and highly-efficient storage of two optical orthogonal polarization modes in a high optical-depth cold atomic ensemble via dynamic EIT process. For achieving a long lifetime in the storage experiment, we follow the two steps, which are used in our previous work (2013 Phys. Rev. Lett. 111 240503). 1) We make the signal and writing-reading light beams collinearly pass through the cold-atom cloud along the z direction to suppress the decoherence between the spin waves due to atomic motion. 2) We apply a moderate magnetic field (13.5 G) to the cold-atom ensemble to lift Zeeman degeneracy. So, the magnetic-field-sensitive transitions are removed from EIT system and the two optical orthogonal polarization modes are stored as two magnetic-field-insensitive spin waves. In contrast to our previous experiment, we finish the storage in the high optical-depth cold atomic ensemble. To obtain such a high optical-depth cold atomic ensemble, we expand the diameters of the trapping laser beams and use a pair of rectangular magnetic coils in a magnetic optical trap (MOT) to prepare a cigar-shaped cold atomic ensemble. The MOT magnetic field is further compressed, and then the optical-depth of the cold atomic ensemble increases up to ~11 in the present experiment, which allows us to achieve a storage efficiency of 30%, which exceeds the previous value (8%). At an MOT repetition rate of 10 Hz, the measured zero-delay storage efficiencies for the two orthogonal polarization modes are symmetric, which go up to ~30%. The 1/e-folding lifetimes of the two orthogonal polarization modes rise up to 3 ms. We also measure the dependence of the zero-delay retrieval efficiency on the MOT repetition rate F and find that the storage efficiency is still more than 20% when the repetition rate F is 50 Hz. The present results will allow one to achieve a long lifetime and highly-efficient quantum memory for photonic polarization qubit and then find applications in scaling-up linear-optical quantum computations and long-distance quantum communication.

A damping term in the theoretical model of our paper [Phys. Rev. A 83, 013827 (2011)] was questioned by the author of the Comment. The author argued this damping term cannot exactly describe the spontaneous decay or quantum jump process and, thus, concluded that our results are prone to be incorrect. However, the physics of electromagnetically induced transparency (EIT) is mainly determined by the ground-state coherence and the optical coherence of the probe transition. We show here that the damping term in our paper described the relaxation process of optical coherence in the EIT system, but not the spontaneous decay process of the population. The case of spontaneous decay used in the argument of the Comment is not an issue in typical EIT studies, in which the probe field is weak and treated as the perturbation. Furthermore, the experimental data in the paper were taken under the condition of a weak probe field. Our theoretical model in the weak-probe condition actually deals with the two coherences of EIT physics, and is suitable for analysis of the data. We believe the results of the study, focusing on the dynamics of slow light and light storage in Doppler-broadened EIT media, are correct.

We propose a "channelization" architecture to achieve wide-band electromagnetically induced transparency (EIT) and ultra-slow light propagation in atomic Rb-87 vapors. EIT and slow light are achieved by shining a strong, resonant "pump" laser on the atomic medium, which allows slow and unattenuated propagation of a weaker "signal" beam, but only when a two-photon resonance condition is satisfied. Our wideband architecture is accomplished by dispersing a wideband signal spatially, transverse to the propagation direction, prior to entering the atomic cell. When particular Zeeman sub-levels are used in the EIT system, then one can introduce a magnetic field with a linear gradient such that the two-photon resonance condition is satisfied for each individual frequency component. Because slow light is a group velocity effect, utilizing differential phase shifts across the spectrum of a light pulse, one must then introduce a slight mismatch from perfect resonance to induce a delay. We present a model which accounts for diffusion of the atoms in the varying magnetic field as well as interaction with levels outside the ideal three-level system on which EIT is based. We find the maximum delay-bandwidth product decreases with bandwidth, and that delay-bandwidth product 1 should be achievable with bandwidth 50 MHz (5 ns delay). This is a large improvement over the 1 MHz bandwidths in conventional slow light systems and could be of use in signal processing applications.

Coherent manipulation of stored images is performed at low light levels based on enhanced cross-Kerr nonlinearity in a four-level N-type electromagnetically induced transparency (EIT) system. Using intensity masks in the signal pulse, quadratic phase shifts with low nonlinear absorption can be efficiently imprinted on the Fraunhofer diffraction patterns already stored in the EIT system. Fast-Fourier-transform-based numerical simulations clearly demonstrate that the far-field images of the retrieved probe light can be flexibly modulated by applying different signal fields. Our studies could help advance the goals of nonlinear all-optical processing for spatial information coherently stored in EIT systems.

Through quantum electrodynamics (QED) we investigate the interactions between a three-level atom and two photon fields under perturbation limit. The dispersion relation and (relative) transmission of the probe photons are obtained by calculating the corresponding Feynman diagrams. The quantum interference in this three-level system such as Fano resonance and electromagnetically induced transparency (EIT) can be tuned by varying the intensities of the control and probe beams. Moreover, by considering that the control beam with periodic modulation, that is, the so-called Landau-Zener-Stückelberg (LZS) type source, the accumulated phase after Landau-Zener transitions is found to show the alternating Fano (EIT) lineshapes in the transmission of the probe photons. We further find that the transmissions can become almost stationary in addition to a wide EIT window in time even though the control beam is a LZS-type oscillating source.

We theoretically predict and experimentally demonstrate chaotic behaviors in a system comprising of three-level atoms inside an optical ring cavity. This electromagnetically induced transparency (EIT) system is driven to chaos through period-doubling route by reducing the frequency detuning of the coupling laser beam. The chaos occurs in a different parametric regime as previously predicted and is believed to be caused by the enhanced dispersion and nonlinearity due to induced atomic coherence in such EIT system.

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.

We study the modified effect of slow-light soliton in a resonant three-level atomic system via electromagnetically induced transparency (EIT) by utilizing a microwave field. We derive a high-order nonlinear Schrodinger equation by using a perturbation method of multiple-scales, and calculate the modification of soliton velocity and frequency shift. We find that in the presence of the microwave field an obvious decrease of propagating velocity of soliton can be realized, which provides an effective method to slow down optical solitons in EIT systems. We also find that the down shift of oscillating frequency of soliton in such system can be largely suppressed by the microwave field.

The possibility of storing and retrieving a single photon of SPDC entangled photon pairs is examined by using electromagnetically induced transparency (EIT). The theory of a proof of principle two-photon interferometer demonstrates new features.

Quantum coherence and interference effects (Scully & Zubairy, 1997) in atomic systems have attracted great attention in the last two decades. With quantum coherence, the absorption and dispersion properties of an optical medium can be extremely modified, and can lead to many important effects such as coherent population trapping (CPT) (Arimondo & Orriols, 1976; Alzetta et al., 1976; Gray et al., 1978), lasing without inversion (LWI) (Harris, 1989; Scully et al., 1989; Padmabandu et al., 1996), electromagnetically induced transparency (EIT) (Boller et al., 1991; Harris, 1997; Ham et al., 1997; Phillips et al., 2003; Fleischhauer et al., 2005; Marangos, 1998), high refractive index without absorption (Scully, 1991; Scully & Zhu, 1992; Harris et al., 1990), giant Kerr effect (Schmidt & Imamoglu, 1996), slow and fast light (Boyd & Gauthier, 2002), light storage (Phillips et al., 2001), and other effects. In particular, EIT plays an important role in the quantum optics area. EIT, named by Harris and his co-workers, has been extensively studied both experimentally and theoretically since it was proposed in 1990 (Harris et al., 1990). Harris et al. first experimentally demonstrated EIT in Sr atomic vapour in 1991 (Boller et al., 1991), providing the basis for further EIT works. Subsequently, M. Xiao and co-workers successfully observed the EIT effect in Rb vapor by using continuous wave (CW) diode lasers (Xiao et al., 1995; Li & Xiao, 1995). This work simplified EIT research, and attracted related research. With the growth of EIT technique, the researchers also realized EIT in several solid state materials and semiconductors (Serapoglia et al., 2000; Zhao et al., 1997; Ham et al., 1997). These works provide a firm foundation for EIT-based applications. One of EIT applications is slow light. Due to the steep dispersion property within the EIT transparency window, EIT can be used to control the group velocity of light. In the past decade, ultraslow group velocity based on EIT (Harris et al., 1992) has drawn much attention to quantum optical applications, such as quantum memories (Liu et al., 2001; Turukhin et al., 2002; Julsgaard et al., 2004), quantum entanglement generations (Lukin & Hemmer, 2000; Petrosyan & Kurizki, 2002; Paternostro et al., 2003), quantum routing (Ham, 2008), and quantum information processing (Nielsen & Chuang, 2000). So far EIT-based slow light has

Comparison of absorption and fluorescence in a nano-cell containing Rb vapor with other Rb nano-cells with addition of neon gas is presented. It is shown that the effect of collapse and revival of Dicke-type narrowing occurs for Rb nanocells containing N2 as buffer gas under 6 and 20 Torr pressure for the thickness L = λ /2 and L = where λ is the resonant λ, laser wavelength 794 nm (D1 line). Particularly for 6 Torr the line-width of the transmission spectrum for the thickness L =λ/2 is 2 times narrower than that for L = λ. For an ordinary Rb cell with L = 0.1 - 10 cm with addition of buffer gas, the velocity selective optical pumping/saturation (VSOP) resonances in saturated absorption spectra are fully suppressed when the buffer gas pressure > 0.5 Torr. A spectacular difference is that for L = λ, VSOP resonances located at the atomic transitions are still observable even when Ne pressure is ≥ 6 Torr. Narrowband fluorescence spectra of a nano-cell with L = λ/2 can be used as a convenient tool for online buffer gas pressure monitoring for the conditions when ordinary pressure gauges are unusable. Comparison of electromagnetically induced transparency (EIT) effect in a nano-cell filled with pure (without a buffer gas) Rb with another nano-cell, where buffer gas nitrogen is added, is presented. The use of N2 gas inside Rb nano-cells strongly extends the range of coupling laser detunings in which it is still possible to form EIT resonance.

Electromagnetically induced transparency (EIT) resonance in strong magnetic fields of up to 1.7 kG has been investigated with the use of a 30-μm cell filled with an atomic rubidium vapor and neon as a buffer gas. The EIT resonance in the Λ system of the D1 line of 85Rb atoms has been formed with the use of two narrowband (∼1 MHz) 795-nm diode lasers. The EIT resonance in a longitudinal magnetic field is split into five components. It has been demonstrated that the frequencies of the five EIT components are either blue- or red-shifted with an increase in the magnetic field, depending on the frequency νP of the probe laser. In has been shown that in both cases the 85Rb atoms enter the hyperfine Paschen-Back regime in magnetic fields of >1 kG. The hyperfine Paschen-Back regime is manifested by the frequency slopes of all five EIT components asymptotically approaching the same fixed value. The experiment agrees well with the theory.

Recently developed thin cells containing atomic vapor of micrometric column thickness L allow one to study peculiarities of Electromagnetically Induced Transparency (EIT) phenomenon, along with the accompanying velocity selective optical pumping/saturation (VSOP) resonances for the case when < 100 μm. The micrometric thin cells (MTC) are filled with pure Rb and neither buffer gas nor paraffin-coated walls were used. The A-systems on D 2 line of 85 Rb have been studied experimentally with the use of bi-chromatic radiation of two separate diode lasers (λ ≃780 nm, γ L ≃ 5MHz). It is demonstrated that when L∼60 μm it is still possible to form the EIT resonance with the sub-natural linewidth ∼ 5 MHz. The EIT resonance linewidth increases up to 10 MHz, when column thickness L is reduced down to Dependence of the EIT resonances are detected in the fluorescence and absorption spectra when the thickness L ∼ 10 μm. Dependence of the EIT resonance linewidth as a function of the atomic vapor column thickness L is presented.