We theoretically report that, utilizing electromagnetically induced transparency (EIT), the transverse spatial properties of weak probe fields can be fast modulated by using optical patterns (e.g. images) with desired intensity distributions in the coupling fields. Consequently, EIT systems can function as high-speed optically addressed spatial light modulators. To exemplify our proposal, we indicate the generation and manipulation of Laguerre-Gaussian beams based on either phase or amplitude modulation in hot vapor EIT systems.
We analyze the influence of dipole-dipole interactions in an electromagnetically induced transparency setup at high density. We show both analytically and numerically that the polarization contribution to the local field strongly modulates the phase of a weak pulse. We give an intuitive explanation for this local field induced phase modulation and show that it distinctively differs from the nonlinear self-phase modulation a strong pulse experiences in a Kerr medium.
We propose an optical double-cavity resonator whose response to a signal is similar to that of an Electromagnetically Induced Transparency (EIT) medium. A combination of such a device with a four-level EIT medium can serve for achieving large cross-Kerr modulation of a probe field by a signal field. This would offer the possibility of building a quantum logic gate based on photonic qubits. We discuss the technical requirements that are necessary for realizing a probe-photon phase shift of Pi caused by a single-photon signal. The main difficulty is the requirement of an ultra-low reflectivity b…
Coherent manipulation of single-photon wave packets is essentially important for optical quantum communication and quantum information processing. In this paper, we realize controllable splitting and modulation of single-photon-level pulses by using a tripod-type atomic medium. The adoption of two control beams enable us to store one signal pulse into superposition of two distinct atomic collective excitations. By controlling the time delay between the two control pulses, we observe splitting of a stored wave packet into two temporally-distinct modes. By controlling the frequency detuning of t…
We present a Maxwell-Bloch description of the dynamics of a light pulse propagating through a spatially inhomogeneous system consisting of alternating layers of EIT media and vacuum. We study the effect of a dynamical modulation of the EIT control field on the shape of the wave packet: interesting effects due to the presence of interfaces with group velocity mismatch are found. An effective description based on a continuity equation is developed. Modulation schemes that can be realized in ultracold atomic samples with standard experimental techniques are proposed and discussed.
We discuss level splitting and sideband transitions induced by a modulated coupling between a superconducting quantum circuit and a nanomechanical resonator. First, we show how to achieve an unconventional time-dependent longitudinal coupling between a flux (transmon) qubit and the resonator. Considering a sinusoidal modulation of the coupling strength, we find that a first-order sideband transition can be split into two. Moreover, under the driving of a red-detuned field, we discuss the optical response of the qubit for a resonant probe field. We show that level splitting induced by modulatin…
The generation of an entangled coherent state is one of the most important ingredients of quantum information processing using coherent states. Recently, numerous schemes to achieve this task have been proposed. In order to generate travelling-wave entangled coherent states, cross phase modulation, optimized by optical Kerr effect enhancement in a dense medium in an electromagnetically induced transparency (EIT) regime, seems to be very promising. In this scenario, we propose a fully quantized model of a double-EIT scheme recently proposed [D. Petrosyan and G. Kurizki, {\sl Phys. Rev. A} {\bf …
We propose a scheme to realize parity-time (PT) symmetry via electromagnetically induced transparency (EIT). The system we consider is an ensemble of cold four-level atoms with an EIT core. We show that the cross-phase modulation contributed by an assisted field, the optical lattice potential provided by a far-detuned laser field, and the optical gain resulted from an incoherent pumping can be used to construct a PT-symmetric complex optical potential for probe field propagation in a controllable way. Comparing with previous study, the present scheme uses only a single atomic species and hence…
We observe electromagnetically induced transparency (EIT) on the 5s to 5p transition in a room temperature rubidium vapour cell by coupling the 5p state to a Rydberg state (ns or nd with n=26 to 124). We demonstrate that the narrow line-width of the EIT resonance (2 MHz) allows precise measurement of the d state fine structure splitting, and together with the sensitivity of the Rydberg state to electric fields, we are able to detect transient electric fields produced by the dynamics of charges within the cell. Coherent coupling of Rydberg states via EIT could also be used for cross-phase modul…
Recently a scheme has been proposed for detection of the structured light by measuring the transmission of a vortex beam through a cloud of cold rubidium atoms with energy levels of the $Λ$-type configuration {[}N. Radwell et al., Phys. Rev. Lett. 114, 123603 (2015){]}. This enables observation of regions of spatially dependent electromagnetically induced transparency (EIT). Here we suggest another scenario for detection of the structured light by measuring the absorption profile of a weak nonvortex probe beam in a highly resonant five-level combined tripod and $Λ$ (CTL) atom-light coupling se…
We propose a method for dynamically controlling the properties of a metamaterial that mimics electromagnetically induced transparency (EIT) by introducing varactor diodes to manipulate the structural symmetry of the metamaterial. Dynamic modulation of the EIT property enables the storage and retrieval of electromagnetic waves. We confirmed that the electromagnetic waves were stored and released, while maintaining the phase distribution in the propagating direction.
Recently, the generation and detection of structured light field have drawn a great deal of attention, due to their importance in high-capacity optical data storage and quantum technology. In this letter, we explore the azimuthal modulation of optical transparency in a four-level double-V type quantum system near a plasmonic nanostructure. A Laguerre-Gaussian beam and the interaction of the system with free-space vacuum modes have been employed to create the phase-dependent absorption of a non-vortex probe field. First, we demonstrate how to identify the azimuthal index associated with the con…
Electromagnetically-induced transparency (EIT) has been proposed as a way to greatly enhance cross-phase modulation, with the possibility of leading to few-photon-level optical nonlinearities. This enhancement grows as the transparency window width, Δ_EIT, is narrowed. Decreasing Δ_EIT, however, increases the response time of the effect, suggesting that for pulses of a given duration, there could be a fundamental limit to the strength of the nonlinearity. We show that in the regimes of most practical interest - narrow EIT windows perturbed by short signal pulses- the enhancement offered by EIT…
We propose a scheme to generate double electromagnetically induced transparency and optimal cross-phase modulation for two slow, copropagating pulses with matched group velocities in a single species of atom, namely 87 Rb. A single pump laser is employed and a homogeneous magnetic field is utilized to avoid cancellation effects through the nonlinear Zeeman effect. We suggest a feasible preparational procedure for the atomic initial state to achieve matched group velocities for both signal fields.
An optical four-level atomic discrete system through optical induction is proposed. A theoretical scheme to produce nonclassical lattice solitons (NLS) in the system is presented with the use of the effects of enhanced self-phase modulation and the giant kerr effect in the electromagnetically induced transparency. The power density and the photon flux can be tuned to a very low level by the controlling field and the soliton can propagate with very slow group velocity. By changing the sign of the detuning $Δ_{1}$, both in-phase and $π$ out-of-phase NLSs can be produced in this system.
We theoretically propose and experimentally demonstrate a parallel-electromagnetically-induced transparency (parallel-EIT) cooling technique for ion crystals in the Paul trap. It has less stringent requirements on the cooling resonance condition than the standard electromagnetically-induced transparency (EIT) cooling, thus allowing, in principle, to simultaneously cool the motional mode spectrum with an arbitrary range. A proof-of-principle validation for this cooling scheme is experimentally demonstrated with up to 4 trapped 40Ca+ ions. We observe simultaneous near-ground-state cooling for al…
We obtain a partial differential equation for a pulse travelling inside a Bose-Einstein condensate under conditions of electromagnetically induced transparency. The equation is valid for a weak probe pulse. We solve the equation for the case of a three-level BEC in $Λ$ configuration with one of its ground state spatial profiles initially constant. The solution characterizes, in detail, the effect that the evolution of the condensate wave function has on pulse propagation, including the process of stopping and releasing it.
We experimentally demonstrate electromagnetically induced transparency and light storage with ultracold 87Rb atoms in a Mott insulating state in a three dimensional optical lattice. We have observed light storage times of about 240 ms, to our knowledge the longest ever achieved in ultracold atomic samples. Using the differential light shift caused by a spatially inhomogeneous far detuned light field we imprint a "phase gradient" across the atomic sample, resulting in controlled angular redirection of the retrieved light pulse.
We study single photon transport in a one-dimensional disordered lattice of three-level atoms coupled to an optical waveguide. In particular, we study atoms of Λ-type that are capable of exhibiting electromagnetically induced transparency (EIT) and separately consider disorder in the atomic positions and transition frequencies. We mainly address the question of how preferential emission into waveguide modes (chirality) can influence the formation of spatially localized states. Our work has relevance to experimental studies of cold atoms coupled to nanoscale waveguides and has possible applicat…
We propose an approach to detect individual Rydberg molecules with each molecule consisting of two atoms in different Rydberg states. The scheme exploits the movement of atoms in the presence of an external force that exerts only on atoms in one Rydberg state. Since the movement of atoms in the other Rydberg state depends on whether they are bound with atoms directly driven by the applied force, bound atoms can be distinguished from unbound atoms. By utilizing electromagnetically induced transparency, it is possible to non-destructively image the positions of molecules. The scheme is sensitive…
Using Electromagnetically Induced Transparency (EIT) in a Cesium vapor, we demonstrate experimentally that the quantum state of a light beam can be mapped into the long lived Zeeman coherences of an atomic ground state. Two non-commuting variables carried by light are simultaneously stored and subsequentely read-out, with no noise added. We compare the case where a tunable single sideband is stored independently of the other one to the case where the two symmetrical sidebands are stored using the same EIT transparency window.
The transmission of a probe field experiencing electromagnetically induced transparency and optical switching in an atomic medium enclosed in an optical cavity is investigated. Using a semiclassical input-output theory for the interaction between an ensemble of four-level atoms and three optical cavity fields coupled to the same spatial cavity mode, we derive the steady-state transmission spectra of the probe field and discuss the dynamics of the intracavity field buildup. The analytical and numerical results are in good agreement with recent experiments with ion Coulomb crystals [M. Albert et…
We present experimental observation of electromagnetically induced transparency (EIT) on a single macroscopic artificial "atom" (superconducting quantum system) coupled to open 1D space of a transmission line. Unlike in a optical media with many atoms, the single atom EIT in 1D space is revealed in suppression of reflection of electromagnetic waves, rather than absorption. The observed almost 100 % modulation of the reflection and transmission of propagating microwaves demonstrates full controllability of individual artificial atoms and a possibility to manipulate the atomic states. The system…
We describe the effect of thermal motion and buffer-gas collisions on a four-level closed N system interacting with strong pump(s) and a weak probe. This is the simplest system that experiences electromagnetically induced absorption (EIA) due to transfer of coherence via spontaneous emission from the excited to ground state. We investigate the influence of Doppler broadening, velocity-changing collisions (VCC), and phase-changing collisions (PCC) with a buffer gas on the EIA spectrum of optically active atoms. In addition to exact expressions, we present an approximate solution for the probe a…
We theoretically investigate a double-Λ electromagnetically induced transparency (EIT) system. The property of the double-Λ medium with a closed-loop configuration depends on the relative phase of the applied laser fields. This phase-dependent mechanism differentiates the double-Λ medium from the conventional Kerr-based nonlinear medium, e.g., EIT-based nonlinear medium discussed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)], which depends only on the intensities of the applied laser fields. Steady-state analytical solutions for the phase-dependent system are obtained by solving the Max…
Dicke narrowing is a phenomena that dramatically reduces the Doppler width of spectral lines, due to frequent velocity-changing collisions. A similar phenomena occurs for electromagnetically induced transparency (EIT) resonances, and facilitates ultra-narrow spectral features in room-temperature vapor. We directly measure the Dicke-like narrowing by studying EIT line-shapes as a function of the angle between the pump and the probe beams. The measurements are in good agreement with an analytic theory with no fit parameters. The results show that Dicke narrowing can increase substantially the to…
Strong nonlinear interactions between single photons have important applications in optical quantum information processing. Demonstrations of these interactions in cold atomic ensembles have largely been limited to exploiting slow light generated using electromagnetically induced transparency (EIT). However, these EIT implementations have limited achievable phase shifts due to spontaneous emission. Here, we demonstrate and characterize a scheme free from these limitations using gradient echo memory with inferred single photon phase shifts of $0.07\pm0.02$ $μ\text{rad}$. Excellent agreement wit…
We study the interaction of a weak probe field, having two orthogonally polarized components, with an optically dense medium of four-level atoms in a tripod configuration. In the presence of a coherent driving laser, electromagnetically induced transparency is attained in the medium, dramatically enhancing its linear as well as nonlinear dispersion while simultaneously suppressing the probe field absorption. We present the semiclassical and fully quantum analysis of the system. We propose an experimentally feasible setup that can induce large Faraday rotation of the probe field polarization an…
Interaction of a control and a signal field with an ensemble of three-level atoms allows direct mapping of the quantum state of the signal field into long lived coherences of an atomic ground state. For a vapor of cesium atoms, using Electromagnetically Induced Transparency (EIT) and Zeeman coherences, we compare the case where a tunable single-sideband is stored independently of the other one to the case where the two symmetrical sidebands are stored using the same transparency window. We study the conditions in which simultaneous storage of two non-commuting variables carried by light and su…
In this paper, we propose a method to generate entangled coherent states between two spatially separated atomic Bose-Einstein condensates (BECs) via the technique of the electromagnetically induced transparency (EIT). Two strong coupling laser beams and two entangled probe laser beams are used to make two distant BECs be in EIT states and to generate an atom-photon entangled state between probe lasers and distant BECs. The two BECs are initially in un-entangled product coherent states while the probe lasers are initially in an entangled state. Entangled states of two distant BECs can be create…
We study the optic control for birefringence of a polarized light by an atomic ensemble with a tripod configuration, which is mediated by the electromagnetically induced transparency with a spatially inhomogeneous laser. The atom ensemble splits the linearly polarized light ray into two orthogonally-polarized components, whose polarizations depend on quantum superposition of the initial states of the atom ensemble. Accompanied with this splitting, the atom ensemble behaves as a birefringent lens, which allows one polarized light ray passing through straightly while focus another orthogonal to …
We present combined measurements of the spatially-resolved optical spectrum and the total excited-atom number in an ultracold gas of three-level atoms under electromagnetically induced transparency conditions involving high-lying Rydberg states. The observed optical transmission of a weak probe laser at the center of the coupling region exhibits a double peaked spectrum as a function of detuning, whilst the Rydberg atom number shows a comparatively narrow single resonance. By imaging the transmitted light onto a charge-coupled-device camera, we record hundreds of spectra in parallel, which are…
People have been paying attention to the role of atoms' complex internal level structures in the research of electromagnetically induced transparency (EIT) for a long time, where the various degenerate Zeeman levels usually generate complex linkage patterns for the atomic transitions. It turns out, with special choices of the atomic states and the atomic transitions' linkage structure, clear signatures of quantum interference induced by the probe and coupling light's polarizations can emerge from a typical EIT phenomena. We propose to study a four state system with double-V linkage pattern for…
We present an experiment using a sample of laser-cooled Rb atoms to show that cross-phase modulation schemes continue to benefit from electromagnetically-induced transparency (EIT) even as the transparency window is made narrower than the signal bandwidth (i.e., for signal pulses much shorter than the response time of the EIT system). Addressing concerns that narrow EIT windows might not prove useful for such applications, we show that while the peak phase shift saturates in this regime, it does not drop, and the time-integrated effect continues to scale inversely with EIT window width. This i…
Dynamic control of a weak quantum probe light pulse for the generation and quantum manipulations of a stationary multi-color (MC-) light field in a resonant coherent atomic medium using electromagnetically induced transparency is proposed. The manipulations have been analyzed based on the analytical solution of the adiabatic limit in the evolution of MC-light fields resulting from interaction of the slow probe light with the new fields generated in the nondegenerate multi-wave mixing scheme. We have found a critical stopping condition for the MC-light fields where the group velocity of light s…
Long-distance quantum optical communications usually require efficient wave-mixing processes to convert the wavelengths of single photons. Many quantum applications based on electromagnetically induced transparency (EIT) have been proposed and demonstrated at the single-photon level, such as quantum memories, all-optical transistors, and cross-phase modulations. However, EIT-based four-wave mixing (FWM) in a resonant double-$Λ$ configuration has a maximum conversion efficiency (CE) of 25% because of absorptive loss due to spontaneous emission. An improved scheme using spatially modulated inten…
We introduce two models of quasi-discrete optical systems: an array of waveguides doped by four-level N-type atoms, and a nonlinear checkerboard pattern, formed by doping with three-level atoms of the Λ-type. The dopant atoms are driven by external fields, to induce the effect of the electromagnetically-induced transparency (EIT). These active systems offer advantages and addition degrees of freedom, in comparison with ordinary passive waveguiding systems. In the array of active waveguides, the driving field may adjust linear and nonlinear propagation regimes for a probe signal. The nonlinear …
Quantum storage and retrieval of light in ion Coulomb crystals using cavity electromagnetically induced transparency is investigated theoretically. It is found that, when both the control and probe fields are coupled to the same cavity mode, their transverse mode profile affects the quantum memory efficiency in a non-trivial way. Under such conditions the control field parameters and crystal dimensions that maximize the memory efficiency are calculated.
Due to coherent population oscillation (CPO) effect, we theoretically examine the generation and manipulation of Laguerre-Gaussian beams in terms of phase and amplitude modulation respectively in semiconductor quantum dots (SQDs). The results indicate that both phase modulation with low absorption of probe field and amplitude modulation with high efficiency can be achieved. Thus the practical way demonstrates that the SQDs system can function as effective optically addressed spatial light modulator with which the transverse spatial properties of probe fields can be artificially modulated.
The interaction of a five-level atomic system involving electromagnetically induced transparency with four light fields is investigated. Two different light-atom configurations are considered, and their efficiency in generating large nonlinear cross-phase shifts compared. The dispersive properties of those schemes are analyzed in detail, and the conditions leading to group velocity matching for two of the light fields identified. An analytical treatment based on amplitude equations is used in order to obtain approximate solutions for the susceptibilities, ehich are shown to fit well with the n…
Reservoir-controlled electromagnetically induced gratings in a weakly driven two-level medium
Abbottabad University of Science and Technology（阿伯塔巴德科学与技术大学）；P. J. Šafárik University（P.J.萨法里克大学）；Government College University（政府学院大学）；Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）
A strong phase modulated coupling field leads to an amplitude modulation of a probe field in an electromagnetically induced transparency process. Time vs. detuning plots for different modulation frequencies reveals a transition between an adiabatic regime where a series of smooth pulses are created with a global phase dependent upon the detuning, and a non-adiabatic regime where a strong transient oscillating response is added to these pulses. In the extreme non-adiabatic regime, where the modulation frequency is higher than the transient decay time, a coherent interference pattern is revealed…
The effect of finite control beam on the transverse spatial profile of the slow light propagation in an electromagnetically induced transparency medium is studied. We arrive at a general criterion in terms of eigenequation, and demonstrate the existence of a set of localized, stationary transverse modes for the negative detuning of the probe signal field. Each of these diffraction-free transverse modes has its own characteristic group velocity, smaller than the conventional theoretical result without considering the transverse spatial effect.
An optical field will undergo coherent diffusion when it is mapped into thermal-motioned atoms, e.g., in a slow or storage light process. As was demonstrated before, such diffusion effect is equivalent to a spatial low-pass filter attenuating the high spatial frequency (SF) components of the optical field. Here, employing electromagnetically induced transparency (EIT) based light storage in hot atomic vapor, we demonstrate that the angular deviation between the control and probe beams could be utilized as a degree of freedom to modulate the SF of the probe beam. The principle is to change the …
We present, experimentally and theoretically, a scheme for dressed-state electromagnetically induced transparency (EIT) in a three-step cascade system where a four-level system is mapped into an effective three-level system. Theoretical analysis reveals that the scheme provides coherent state control via adiabatic following and provides a generalized protocol for light storage in uniform phase spin-waves that are insensitive to motional dephasing. The three-step driving enables a number of other features including spatial selectivity of the excitation region within the atomic medium, and kick-…
Electromagnetically induced transparency (EIT) in atomic systems involving Rydberg states is known to be a sensitive probe of incident microwave (MW) fields, in particular those resonant with Rydberg-to-Rydberg transitions. Here we propose an intelligible analytical model of Rydberg atomic receiver's response to amplitude- (AM) and frequency-modulated (FM) signals, and compare it with experimental results: we present a setup that allows sending signals with either AM or FM and evaluating their efficiency with demodulation. Additionally, the setup reveals a new detection configuration, using al…
The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac materials can give rise to localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) confinement possible depending on the geometry of the velocity modulation. We present several exactly solvable models illustrating the nature of the bound states which arise, revealing how the gradient of the Fermi velocity is crucial fo…
We have recently shown that Alkali atoms contained in a vapor cell can serve as a highly accurate standard for microwave electric field strength as well as polarization using the principles of Rydberg atom electromagnetically induced transparency. Here, we show, for the first time, that Rydberg atom electromagnetically induced transparency can be used to image microwave electric fields with unprecedented precision. The spatial resolution of the method is far into the sub-wavelength regime. The electric field resolutions are similar to those we have demonstrated in our prior experiments. Our ex…
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）；Department of Physics and Hong Kong Institute of Quantum Science and Technology, The University of Hong Kong（香港大学物理系香港量子科学技术研究院）
We demonstrate nanometer-scale spatial control of inter-atomic interactions in a Bose-Einstein condensate of ytterbium(Yb). A pulsed optical standing wave, tuned near an optical Feshbach resonance varies the s-wave scattering length continuously across the standing wave pattern. The modulated mean-field energy with a spatial period of every 278 nm is monitored by a diffraction pattern in a time-of-flight image. We observe a wide scattering length control of up to 160 nm. The demonstrated spatial modulation of the scattering length proves that the high resolution control of atomic interactions …
In this paper we propose a dark-state-based trapping strategy to break the optical diffraction limit for microscopy. We utilize a spatially dependent coupling field and a probe laser field with temporal and spatial modulation to interact with three-level atoms. The temporal modulation allows us to reduce the full width at half maximum (FWHM) of point spread function, and the spatial modulation help us obtain better spatial resolution than Gaussian beam. In addition, we also propose a proof-of-principle experiment protocol and discuss its feasibility.
