Slow light, superadiabaticity and shape-preserving pulses

Ultrafast slow-light: Raman-induced delay of THz-bandwidth pulses

We propose and experimentally demonstrate a scheme to generate optically-controlled delays based on off-resonant Raman absorption. Dispersion in a transparency window between two neighboring, optically-activated Raman absorption lines is used to reduce the group velocity of broadband 765 nm pulses. We implement this approach in a potassium titanyl phosphate (KTP) waveguide at room temperature, and demonstrate Raman-induced delays of up to 140 fs for a 650-fs duration, 1.8-THz bandwidth, signal pulse; the available delay-bandwidth product is $\approx1$. Our approach is applicable to single phot…

Slow light in three-level cold atoms: a numerical analysis

We investigate theoretically the slow group velocity of a pulse probe laser propagating through a cold sample and interacting with atoms in a three-level $Λ$ configuration having losses towards external states. The EIT phenomenon produces very small group velocities for the probe pulse in presence of a strong coupling field even in presence of the population losses, as in an open three-level system. The group velocity and the transmission of the pulses are examined numerically as functions of several parameters, the adiabatic transfer, the loss rate, the modification of the atomic velocity pro…

慢光波导中通过和频转换实现单光子波包的光谱压缩

Spectral compression of single-photon wave packets by sum-frequency conversion in slow-light waveguides

本文提出一种慢光波导方案，通过和频产生同时实现弱光脉冲（含单光子态）的频率转换与光谱压缩，理论表明可将3 ps脉冲压缩至纳秒量级，压缩因子约1000，本征效率最高83%，且输出脉冲形状适合光学腔时间模式匹配。

Coherent propagation of a single photon in a lossless medium: $0π$ pulse formation, slow photon, storage and retrieval in multiple temporal modes

Single-photon coherent optics represents a fundamental importance for the investigation of quantum light-matter interactions. While most work has considered the interaction in the steady-state regime, here we demonstrate that a single-photon pulse shorter than any relaxation time in a medium propagates without energy loss and is consistently transformed into a zero-area pulse. A general analytical solution is found for photon passage through a cold ensemble of $Λ$-type atoms confined inside a hollow core of a single-mode photonic-crystal fiber. We use the robust far off-resonant Raman scheme t…

Nonlinear Optics and Quantum Entanglement of Ultra-Slow Single Photons

Two light pulses propagating with ultra-slow group velocities in a coherently prepared atomic gas exhibit dissipation-free nonlinear coupling of an unprecedented strength. This enables a single-photon pulse to coherently control or manipulate the quantum state of the other. Processes of this kind result in generation of entangled states of radiation field and open up new prospectives for quantum information processing.

Low-light-level nonlinear optics with slow light

Electromagnetically induced transparency in an optically thick, cold medium creates a unique system where pulse-propagation velocities may be orders of magnitude less than $c$ and optical nonlinearities become exceedingly large. As a result, nonlinear processes may be efficient at low-light levels. Using an atomic system with three, independent channels, we demonstrate a quantum interference switch where a laser pulse with an energy density of $\sim23$ photons per $λ^2/(2π)$ causes a 1/e absorption of a second pulse.

Matched Slow Pulses Using Double Electromagnetically Induced Transparency

We implement double electromagnetically-induced transparency (double EIT) in rubidium vapor, using a tripod-shaped energy level scheme consisting of hyperfine and magnetic sublevels of the 5S1/2 to 5P1/2 transition. We show experimentally that through the use of double EIT one can control the contrast of transparency windows as well as group velocities of the two signal fields. In particular, the group velocities can be equalized, which holds promise to greatly enhance nonlinear optical interaction between these fields.

Dynamical Decoupling Using Slow Pulses: Efficient Suppression of 1/f Noise

The application of dynamical decoupling pulses to a single qubit interacting with a linear harmonic oscillator bath with $1/f$ spectral density is studied, and compared to the Ohmic case. Decoupling pulses that are slower than the fastest bath time-scale are shown to drastically reduce the decoherence rate in the $1/f$ case. Contrary to conclusions drawn from previous studies, this shows that dynamical decoupling pulses do not always have to be ultra-fast. Our results explain a recent experiment in which dephasing due to $1/f$ charge noise affecting a charge qubit in a small superconducting el…

Storage and retrieval of light pulses in atomic media with "slow" and "fast" light

We present experimental evidence that light storage, i.e. the controlled release of a light pulse by an atomic sample dependent on the past presence of a writing pulse, is not restricted to small group velocity media but can also occur in a negative group velocity medium. A simple physical picture applicable to both cases and previous light storage experiments is discussed.

Slow light with integrated gain and large pulse delay

We demonstrate slow and stored light in Rb vapor with a combination of desirable features: minimal loss and distortion of the pulse shape, and large fractional delay (> 10). This behavior is enabled by: (i) a group index that can be controllably varied during light pulse propagation; and (ii) controllable gain integrated into the medium to compensate for pulse loss. Any medium with the above two characteristics should be able to realize similarly high-performance slow light.

Quantum key distribution protocols with slow basis choice

Many quantum key distribution (QKD) protocols require random choice of measurement basis for each pulse or each train of pulses. In some QKD protocols, such as the Round-Robin Differential Phase Shift (RRDPS) QKD protocol, this requirement is a bit challenging as randomly choosing hundreds of settings for every, say, 100 pulses may be too fast with current technologies. In this paper, we solve this issue by proving the security of QKD protocols with slow basis choice without compromising the secret key rate. We also show that the random choice of the bases for the state preparation can be made…

Light slowdown in the vicinity of cross-over resonances

Pulse propagation is considered in an inhomogeneously broadened medium of three-level atoms in a V-configuration, dressed by a counter-propagating pump pulse. A significant signal slowdown is demonstrated in this of the three frequency windows of a reduced absorption and a steep normal dispersion, which is due to a cross-over resonance. Particular properties of the group index in the vicinity of such a resonance are demonstrated in the case of closely spaced upper levels.

Slow and stored light and optical depth

We present a preliminary experimental study of the dependence on optical depth of slow and stored light pulses in Rb vapor. In particular, we characterize the efficiency of slow and stored light as a function of Rb density; pulse duration, delay and storage time; and control field intensity. Experimental results are in good qualitative agreement with theoretical calculations based on a simplified three-level model at moderate densities.

Dispersive effects on optical information storage in Bose-Einstein condensates with ultra-slow short pulses

We investigate the potential of atomic Bose-Einstein condensates as dynamic memory devices for coherent optical information processing. Specifically, the number of ultraslow pulses that can be simultaneously present within the storage time in the condensate has been analyzed. By modeling short-pulse propagation through the condensate, taking into account high-order dispersive properties, constraints on the information storage capacity are discussed. The roles of temperature, spatial inhomogeneity, the interatomic interactions, and the coupling laser on the pulse shape are pointed out. For a re…

Slow light in paraffin-coated Rb vapor cells

We present preliminary results from an experimental study of slow light in anti-relaxation-coated Rb vapor cells, and describe the construction and testing of such cells. The slow ground state decoherence rate allowed by coated cell walls leads to a dual-structured electromagnetically induced transparency (EIT) spectrum with a very narrow (<100 Hz) transparency peak on top of a broad pedestal. Such dual-structure EIT permits optical probe pulses to propagate with greatly reduced group velocity on two time scales. We discuss ongoing efforts to optimize the pulse delay in such coated cell system…

Causality and information transfer in simultaneously slow- and fast-light media

We demonstrate the simultaneous propagation of slow- and fast-light optical pulses in a four-wave mixing scheme using warm potassium vapor. We show that when the system is tuned such that the input probe pulses exhibit slow-light group velocities and the generated pulses propagate with negative group velocities, the information velocity in the medium is nonetheless constrained to propagate at, or less than, c. These results demonstrate that the transfer and copying of information on optical pulses to those with negative group velocities obeys information causality, in a manner that is reminisc…

Adiabatic pulse propagation in coherent atomic media with the tripod level configuration

We investigate the problem of propagation of three-component resonant light pulses with adiabatically varying amplitudes through a medium consisting of atoms with the tripod level configuration. By means of both analytic and numerical methods we found the two modes of shape-preserving pulse propagation. The pulse propagation velocity is found to be either equal to the speed of light or significantly slowed down, depending on a particular propagation mode.

Slow Light amplification in a non-inverted gain medium

We investigate the propagation of a coherent probe light pulse through a three-level atomic medium (in the $Λ$--configuration) in the presence of a pump laser under the conditions for gain without inversion. When the carrier frequency of the probe pulse and the pump laser are in a Raman configuration, we show that it is possible to amplify a slow propagating pulse. We also analyze the regime in which the probe pulse is slightly detuned from resonance where we observe anomalous light propagation.

Spectral Engineering of Slow Light, Cavity Line Narrowing, and Pulse Compression

More than 4 orders of magnitude of cavity-linewidth narrowing in a rare-earth-ion-doped crystal cavity, emanating from strong intracavity dispersion caused by off-resonant interaction with dopant ions, is demonstrated. The dispersion profiles are engineered using optical pumping techniques creating significant semipermanent but reprogrammable changes of the rare-earth absorption profiles. Several cavity modes are shown within the spectral transmission window. Several possible applications of this phenomenon are discussed.

Electromagnetically induced transparency and nonlinear pulse propagation in a combined tripod and $Λ$ atom-light coupling scheme

We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda ($Λ$) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional $Λ$- or $N$-type atom-light couplings providing the EIT or absorption, respectively. Thus the atomic system can experi…

Slow light in flight imaging

Slow-light media are of interest in the context of quantum computing and enhanced measurement of quantum effects, with particular emphasis on using slow-light with single photons. We use light-in-flight imaging with a single photon avalanche diode camera-array to image in situ pulse propagation through a slow light medium consisting of heated rubidium vapour. Light-in-flight imaging of slow light propagation enables direct visualisation of a series of physical effects including simultaneous observation of spatial pulse compression and temporal pulse dispersion. Additionally, the single-photon …

Slow light propagation and amplification via electromagnetically induced transparency and four-wave mixing in an optically dense atomic vapor

We experimentally and theoretically analyze the propagation of weak signal field pulses under the conditions of electromagnetically induced transparency (EIT) in hot Rb vapor, and study the effects of resonant four-wave mixing (FWM). In particular, we demonstrate that in a double-$Λ$ system, formed by the strong control field with the weak resonant signal and a far-detuned Stokes field, both continuous-wave spectra and pulse propagation dynamics for the signal field depend strongly on the amplitude of the seeded Stokes field, and the effect is enhanced in optically dense atomic medium. We also…

Observations of time delayed all-optical routing in a slow light regime

We report an observation of a delayed all-optical routing/switching phenomenon based on ultraslow group velocity of light via nondegenerate four-wave mixing processes in a defected solid medium. Unlike previous demonstrations of enhanced four-wave mixing processes using the slow light effects, the present observation demonstrates a direct retrieval of the resonant Raman-pulse excited spin coherence into photon coherence through coherence conversion processes.

利用电磁诱导透明在热碱金属蒸气中产生慢光

Producing slow light in warm alkali vapor using electromagnetically induced transparency

本研究提供了适合本科生的实验指导，利用电磁诱导透明（EIT）在热铷蒸气中产生比光速慢近百万倍的慢光，介绍了装置与脉冲制备细节，可为量子技术相关学习研究提供基础参考。

Many-body physics of slow light

We present a quantum theory of slow light beyond the weak probe pulse approximation. By reduction of the full Hamiltonian of the system to an effective Hamiltonian for a single quantum field we demonstrate that the concept of dark-state polaritons can be introduced even if the linearized approach is no longer valid. The developed approach allows us to study the evolution of non-classical quantum states of the polariton field.

Propagation of Raman-matched laser pulses through a Bose-Einstein condensate

We investigate the role of non-uniform spatial density profiles of trapped atomic Bose-Einstein condensates in the propagation of Raman-matched laser pulses under conditions for electromagnetically induced transparency (EIT). We find that the sharp edged axial density profile of an interacting condensate (due to a balance between external trap and repulsive atomic interaction) is advantageous for obtaining ultra slow averaged group velocities. Our results are in good quantitative agreement with a recent experiment report [Nature {\bf 397}, 594 (1999)].

Decoherence-free propagation and ramification of a solitary pulse

Using a microscopic master equation to account for the environmental effects, we compute the decoherence culminated during the propagation of a microwave pulse of arbitrary shape through a superconducting qubit. It is shown that the qubit decoherence vanishes and the pulse shape remains absorption-free when the latter adopts a soliton shape with $nπ$ area. Otherwise, the environmental feedback decelerates the velocity of the soliton envelop and induces an monotonic increase of phase in the microwave. A pulse of non-$nπ$ area thus ramifies into a transparent part that travels decoherence-free a…

Storing and processing optical information with ultra-slow light in Bose-Einstein condensates

We theoretically explore coherent information transfer between ultra-slow light pulses and Bose-Einstein condensates (BECs) and find that storing light pulses in BECs, by switching off the coupling field, allows the coherent condensate dynamics to process optical information. We develop a formalism, applicable in both the weak and strong probe regimes, to analyze such experiments and establish several new results. Investigating examples relevant to Rb-87 experimental parameters we see a variety of novel two-component BEC dynamics occur during the storage, including interference fringes, gentle…

Coherent Control of Stationary Light Pulses

We present a detailed analysis of the recently demonstrated technique to generate quasi-stationary pulses of light [M. Bajcsy {\it et al.}, Nature (London) \textbf{426}, 638 (2003)] based on electromagnetically induced transparency. We show that the use of counter-propagating control fields to retrieve a light pulse, previously stored in a collective atomic Raman excitation, leads to quasi-stationary light field that undergoes a slow diffusive spread. The underlying physics of this process is identified as pulse matching of probe and control fields. We then show that spatially modulated contro…

Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas

We experimentally study the group time delay for a light pulse propagating through hot Rb vapor in the presence of a strong coupling field in a $Λ$ configuration. We demonstrate that the ultra-slow pulse propagation is transformed into superluminal propagation as the one-photon detuning of the light increases due to the change in the transmission resonance lineshape. Negative group velocity as low as -c/10^6=-80 m/s is recorded. We also find that the advance time in the regime of the superluminal propagation grows linearly with increasing laser field power.

Instantaneous processing of "slow light": amplitude-duration control, storage, and splitting

Nonadiabatic change of the control field or of the low-frequency coherence allows for an almost instantaneous change of the signal field propagating in a thick resonant absorber where electromagnetically induced transparency is realized. This finding is applied for the storage and retrieval of the signal, for the creation of a signal copy and separation of this copy from the original pulse without its destruction.

Polarization properties of 'slow' light

The propagation of the arbitrarily polarized pulse of the weak probe field through the resonant medium of Lambda-type three-level atoms with degenerate levels adiabatically driven by the coherent coupling field is considered. It is shown that such pulse is decomposed in the medium into two orthogonally polarized dark-state polaritons propagating with different group velocities. The expressions for the polarizations and group velocities of these two polaritons are obtained. The dependence of these polarizations and group velocities on the values of the angular momenta of resonant levels, on the…

Slow light based optical frequency shifter

We demonstrate experimentally and theoretically a controllable way of shifting the frequency of an optical pulse by using a combination of spectral hole burning, slow light effect, and linear Stark effect in a rare-earth-ion doped crystal. We claim that the solid angle of acceptance of a frequency shift structure can be close to $2π$, which means that the frequency shifter could work not only for optical pulses propagating in a specific spatial mode but also for randomly scattered light. As the frequency shift is controlled solely by an external electric field, it works also for weak coherent …

子波长调制波导中强非线性慢光极子

Strongly Nonlinear Slow Light Polaritons in Subwavelength Modulated Waveguides

研究通过设计低群速和群速色散的介质超晶格结构，实现强光物质相互作用下的慢光，显著增强非线性效应，推动少光子量子领域发展。

Controllable ultra-broadband slow light in a warm Rubidium vapor

We study ultra-broadband slow light in a warm Rubidium vapor cell. By working between the D1 and D2 transitions, we find a several-nm window centered at 788.4 nm in which the group index is highly uniform and the absorption is small (<1%). We demonstrate that we can control the group delay by varying the temperature of the cell, and observe a tunable fractional delay of 18 for pulses as short as 250 fs (6.9 nm bandwidth) with a fractional broadening of only 0.65 and a power leakage of 55%. We find that a simple theoretical model is in excellent agreement with the experimental results. Using th…

Electromagnetically Induced Transparency and slow light in media with Rydberg Excitons

We show that the Electromagnetically Induced Transparency (EIT) is possible in a medium exhibiting Rydberg excitons and indicate the realistic parameters to perform the experiment. The calculations for a Cu$_2$O crystal are given which show that in this medium due to large group index one could expect slowing down a light pulse by a factor about $10^4$.

Stationary and quasi-stationary light pulse in three-level cold atomic system

We have studied stationary and quasi-stationary signal light pulses in cold lambda-type atomic media driven by counterpropagating control laser fields at the condition of electromagnetically induced transparency. By deriving a dispersion relation we present spectral and temporal properties of the signal light pulse and a significant influence of atomic decoherence on the coupled stationary light pulses for spatial splitting. Finally we discuss quasi-stationary light pulse evolution characterized by frozen spatial spreading for a robust coherent control of slow light pulses.

Propagation of subcycle pulses in a two-level medium: Area-theorem breakdown and pulse shape

We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly-varying-envelope approximations. The method of solution is based on the Maxwell--Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pu…

Quantum Control in Qutrit Systems using Hybrid Rabi-STIRAP Pulses

We introduce and analyze theoretically a procedure that combines slow adiabatic STIRAP manipulation with short nonadiabatic Rabi pulses to produce any desired three-level state in a qutrit system. In this protocol, the fast pulses create superpositions between the ground state and the first excited state, while the slow pulses transfer an arbitrary population to the second excited state via stimulated Raman adiabatic passage (STIRAP). We demonstrate high-fidelity quantum control of the level populations and phases and we characterize the errors incurred under the breakdown of adiabaticity. In …

Efficient all-optical switching using slow light within a hollow fiber

We demonstrate a fiber-optical switch that is activated at tiny energies corresponding to few hundred optical photons per pulse. This is achieved by simultaneously confining both photons and a small laser-cooled ensemble of atoms inside the microscopic hollow core of a single-mode photonic-crystal fiber and using quantum optical techniques for generating slow light propagation and large nonlinear interaction between light beams.

Diffraction of strongly interacting molecular Bose-Einstein condensate from standing wave light pulses

We study the effects of strong inter-particle interaction on diffraction of a Bose-Einstein condensate of $^6Li_2$ molecules from a periodic potential created by pulses of a far detuned optical standing wave. For short pulses we observe the standard Kapitza-Dirac diffraction, with the contrast of the diffraction pattern strongly reduced for very large interactions due to interaction dependent loss processes. For longer pulses diffraction shows the characteristic for matter waves impinging on an array of tubes and coherent channeling transport. We observe a slowing down of the time evolution go…