We consider theoretically a driven-dissipative quantum many-body system consisting of an atomic ensemble in a single-mode optical cavity as described by the open Tavis-Cummings model. In this hybrid light-matter system the interplay between coherent and dissipative processes leads to superradiant pulses with a build-up of strong correlations, even for systems comprising hundreds to thousands of particles. A central feature of the mean-field dynamics is a self-reversal of two spin degrees of freedom due to an underlying time-reversal symmetry, which is broken by quantum fluctuations. We demonstrate a quench protocol that can maintain highly non-Gaussian states over long time scales. This general mechanism offers interesting possibilities for the generation and control of complex fluctuation patterns, as suggested for the improvement of quantum sensing protocols for dissipative spin-amplification.
We discuss the passage-time statistics of superradiant light pulses generated during the scattering of laser light from an elongated atomic Bose-Einstein condensate. Focusing on the early-stage of the phenomenon, we analyze the corresponding probability distributions and their scaling behaviour with respect to the threshold photon number and the coupling strength. With respect to these parameters, we find quantities which only vary significantly during the transition between the Kapitza Dirac and the Bragg regimes. A possible connection of the present observations to Brownian motion is also di…
A recent experiment demonstrated heterodyne detection-based frequency measurements with superradiant pulses from coherently pumped strontium atoms in an optical lattice clock system, while another experiment has analyzed the statistics of superradiant pulses from incoherently pumped calcium atoms in a similar system. In this article, we propose to perform heterodyne detection of the superradiant pulses from the calcium atoms, and analyze theoretically the corresponding atomic ensemble dynamics in terms of the rotation of a collective spin vector and the incoherent quantum jumps among superradi…
Lasing in the bad cavity regime has promising applications in precision metrology due to the reduced sensitivity to cavity noise. Here we investigate the spectral properties and phase behavior of pulsed lasing on the $^1$S$_0 - ^3$P$_1$ line of $^{88}$Sr in a mK thermal ensemble, as first described in arxiv:1903.12593. The system operates in a regime where the Doppler-broadened atomic transition linewidth is several times larger than the cavity linewidth. We find that by detuning the cavity resonance, the influence of the cavity noise on the peak lasing frequency can be eliminated to first ord…
We present experimental evidence supporting the postulation that the secondary effects of light-assisted collisions are the main reason that the superradiant light scattering efficiency in condensates is asymmetric with respect to the sign of the pump-laser detuning. Contrary to the recent experimental study, however, we observe severe and comparable heating with all three pump-laser polarizations. We also perform two-color, double-pulse measurements to directly study the degradation of condensate coherence and the resulting impact on the superradiant scattering efficiency.
Due to its coherence properties and high optical depth, a Bose-Einstein condensate provides an ideal setting to investigate collective atom-light interactions. Superradiant light scattering in a Bose-Einstein condensate is a fascinating example of such an interaction. It is an analogous process to Dicke superradiance, in which an electronically inverted sample decays collectively, leading to the emission of one or more light pulses in a well-defined direction. Through time-resolved measurements of the superradiant light pulses emitted by an end-pumped BEC, we study the close connection of supe…
We investigate the stimulated emission of superradiant atoms coupled to a waveguide induced by a coherent-state photon pulse. We provide an analytical result when a short $π$ pulse is incident, which shows that the atoms emit photons coherently into the output pulse, which remains a coherent state in the short pulse limit. An incident pulse is amplified in phase-preserving manner, where noise is added almost entirely in the phase direction in phase space. This property improves the ratio of intensity signal to noise after the amplification for sufficiently short pulses. This is a unique featur…
We show that in the strong coupling linear regime, the dispersive opto-mechanical Hamiltonian system can undergo a Dicke-Hepp-Lieb superradiant phase transition with two critical points. The higher critical point is the usual second order Dicke superradiant phase transition while the lower critical point is a new effect showing similarity to the usual Dicke superradiance. We also show that the mechanical mode near its quantum ground state completely decouples from the optical mode and the optical mode shows similarity to the Bogoluibov like excitations.
We propose a single-atom, cavity quantum electrodynamics system, compatible with recently demonstrated, fiber-integrated micro- and nano-cavity setups, for the on-demand production of optical number-state, $0N$-state, and binomial-code-state pulses. The scheme makes use of Raman transitions within an entire atomic ground-state hyperfine level and operates with laser and cavity fields detuned from the atomic transition by much more than the excited-state hyperfine splitting. This enables reduction of the dynamics to that of a simple, cavity-damped Tavis-Cummings model with the collective spin d…
The propagation of a step pulse through a thick resonant absorber with homogeneously broadened absorption line is considered. It is shown that a specific subradiant state is naturally developed in the absorber due to the formation of the spatial domains of the atomic coherence with opposite phases. It is proposed to divide the absorber into slices in accord with these domains and place the phase shifters in front of the first slice and between the other slices. If the phase shifters are switched on simultaneously at a particular moment of time, elapsed from the beginning of the step pulse, a s…
We develop a stochastic mean-field theory to describe active frequency measurements of pulsed superradiant emission, studied in recent experiments with strontium-87 atoms trapped in an optical lattice inside an optical cavity [M. Norcia, et al., Phys. Rev. X 8, 21036 (2018)]. Our theory reveals the intriguing dynamics of atomic ensembles with multiple transition frequencies, and it reproduces the superradiant beats signal, noisy power spectra, and frequency uncertainty in remarkable agreement with the experiments. Moreover, by reducing the number of atoms, elongating the superradiant pulses an…
We propose a superradiant metrology technique to achieve the Heisenberg limit super-resolving displacement measurement by encoding multiple light momenta into a three-level atomic ensemble. We use $2N$ coherent pulses to prepare a single excitation superradiant state in a superposition of two timed Dicke states that are $4N$ light momenta apart in momentum space. The phase difference between these two states induced by a uniform displacement of the atomic ensemble has $1/4N$ sensitivity. Experiments are proposed in crystals and in ultracold atoms.
We theoretically discuss several aspects of sequential superradiant scattering from atomic Bose-Einstein condensates. Our treatment is based on the semiclassical description of the process in terms of the Maxwell-Schroedinger equations for the coupled matter-wave and optical fields. First, we investigate sequential scattering in the weak-pulse regime and work out the essential mechanisms responsible for bringing about the characteristic fan-shaped side-mode distribution patterns. Second, we discuss the transition between the Kapitza-Dirac and Bragg regimes of sequential scattering in the stron…
We report the results of the first investigation on the superradiant temporal and spatial quantum dynamics of two dipoles excited in a planar symmetrical microcavity by a controlled femtosecond two-pulse excitation. A superradiant enhancement of the time decay of the dipole excitation for a decreasing inter-dipole transverse distance R has been found. Furthermore, the photon partition statistics of the emitted field is found to exhibit a striking quantum behaviour for R<lc, the transverse extension of the single allowed microcavity mode.
The modification of initially entangled light pulses passing through dispersive and absorbing four-port devices is studied, using recently obtained results on quantum state transformations [Phys. Rev. A 59, 4716 (1999)]. The fidelity and indices of quantum correlations based on the von Neumann entropy are calculated. Their dependence on both the pulse shape and the four-port device parameters is studied. It is shown, that due to dispersion and absorption the quantum correlations are reduced substantially for large initial entanglement.
Recent experiments have demonstrated Rabi-oscillations, superradiant pulses and stimulated emission from negatively-charged nitrogen-vacancy ($\mathrm{NV}^{-}$) center spins in microwave resonators. These phenomena witness the kind of collective and strong coupling which has been prerequisite for observation of superradiant lasing in the optical frequency regime. In this article, we investigate the possibility to employ coherence, present in both the collective $\mathrm{NV}^{-}$ spin ensemble and the microwave field, to achieve a superradiant maser. Our calculations show that a superradiant ma…
Laser cooled and quantum degenerate atoms are widely being pursued as quantum simulators that may explain the behavior of strongly correlated material systems, and as the basis of today's most precise sensors. A key challenge towards these goals is to understand and control coherent interactions between the atoms. Here, we observe long-range exchange interactions mediated by an optical cavity, which manifest as tunable spin-spin interactions on the pseudo spin-1/2 system composed of the millihertz linewidth clock transition in strontium. We observe the so-called one axis twisting dynamics, the…
We investigate the causal propagation of the pulse through dispersive media by very precise numerical solution of the coupled Maxwell-Bloch equations without any approximations about the strength of the input field. We study full nonlinear behavior of the pulse propagation through solid state media like ruby and alexandrite. We have demonstrated that the information carried by the discontinuity, {\it i.e}, front of the pulse, moves inside the media with velocity $c$ even though the peak of the pulse can travel either with sub-luminal or with super-luminal velocity. We extend the argument of Le…
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…
We demonstrate a dispersive measurement pulse shaping technique that allows for arbitrarily fast quantum non-demolition, single-quadrature measurements of non-linear systems and unconditionally leaves the measurement resonator empty. For single-qubit measurements, current measurements are limited to the 99% fidelity range due to relaxation during the process. However, trying to go to shorter times to circumvent this with square or composite digital pulses leads to leftover cavity population after measurement of the same order of error. These effects can be suppressed using simple smooth pulse …
An efficient technique to produce a periodic sequence of ultrashort pulses of recoilless gamma-radiation via its transmission through the optically thick vibrating resonant absorber was demonstrated recently [Nature, 508, 80 (2014)]. In this work we extend the theoretical analysis to the case of a set of multiple absorbers. We consider an analytical model describing the control of spectral content of a frequency modulated gamma-radiation by selective correction of amplitudes and initial phases of some spectral components, using, respectively, the resonant absorption or dispersion of nuclei. On…
We demonstrate the non-dispersive deflection of an optical beam in a Stern-Gerlach magnetic field. An optical pulse is initially stored as a spin-wave coherence in thermal rubidium vapour. An inhomogeneous magnetic field imprints a phase gradient onto the spin wave, which upon reacceleration of the optical pulse leads to an angular deflection of the retrieved beam. We show that the obtained beam deflection is non-dispersive, i.e. its magnitude is independent of the incident optical frequency. Compared to a Stern-Gerlach experiment carried out with propagating light under the conditions of elec…
Active Optical Frequency Measurements with Superradiance Prolonged by a Modulated Magnetic Field
Zhengzhou University（郑州大学）；University of Copenhagen（哥本哈根大学）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Henan Academy of Sciences（河南省科学院）
We present simulations of the superradiant dynamics of ensembles of atoms in the presence of collective and individual atomic decay processes. We unravel the density matrix with Monte-Carlo wave-functions and identify the quantum jumps in a reduced Dicke state basis, which reflects the permutation symmetry of the identical atoms. While the number of density matrix elements in the Dicke representation increases polynomially with atom number, the quantum jump dynamics populates only a single Dicke state at the time and thus efficient simulations can be carried out for tens of thousands of atoms.…
We show that a collection of two-level atoms in an optical cavity beyond the rotating wave approximation and in the dispersive and strong-coupling regime constitutes a nonlinear medium and is capable of generating squeezed state of light. It is found that squeezing produced in the strong-coupling regime is significantly higher compared to that produced in the dispersive limit. On the other hand, we also show that it could be possible to observe the Dicke superradiant quantum phase transition in the dispersive regime where the vector potential term is negligible. Such a system can be an essenti…
Based on the similarity of paraxial diffraction and dispersion mathematical descriptions, the temporal imaging of optical pulses combines linear dispersive filters and quadratic phase modulations operating as time lenses. We consider programming a dispersive filter near atomic resonance in rare earth ion doped crystals, which leads to unprecedented high values of dispersive power. This filter is used in an approximate imaging scheme, combining a single time lens and a single dispersive section and operating as a time reversing device, with potential applications in radio-frequency signal proce…
The cooling performance of an optomechanical system comprising both dispersive and dissipative coupling is studied. We present a scheme to cool a mechanical resonator to its ground state in finite time by employing a chirped pulse. When the cavity damping strength increases, the phonon occupation of the resonator will decrease. Moreover, the cooling behaviors of this dispersively and dissipatively coupled system with different incident pulses, different system coupling strengths are explored. Our scheme is feasible to cool the resonator in a wide parameter region.
We establish a testbed system for the development of high-sensitivity Electron Spin Resonance (ESR) techniques for small samples at cryogenic temperatures. Our system consists of a Niobium Nitride thin-film planar superconducting microresonator designed to have a concentrated mode volume to couple to a small amount of paramagnetic material, and to be resilient to magnetic fields of up to 400 mT. At 65 mK we measure high-cooperativity coupling ($C \approx 19$) to an organic radical microcrystal containing $10^{12}$ spins in a pico-litre volume. We detect the spin-lattice decoherence rate via th…
Superradiance is the archetypical collective phenomenon where radiation is amplified by the coherence of emitters. It plays a prominent role in optics, where it enables the design of lasers with substantially reduced linewidths, quantum mechanics, and is even used to explain cosmological observations like Hawking radiation from black holes. Hybridization of distinct quantum systems allows to engineer new quantum metamaterials pooling the advantages of the individual systems. Superconducting circuits coupled to spin ensembles are promising future building blocks of integrated quantum devices an…
Recently proposed quantum-chaotic sensors achieve quantum enhancements in measurement precision by applying nonlinear control pulses to the dynamics of the quantum sensor while using classical initial states that are easy to prepare. Here, we use the cross-entropy method of reinforcement learning to optimize the strength and position of control pulses. Compared to the quantum-chaotic sensors with periodic control pulses in the presence of superradiant damping, we find that decoherence can be fought even better and measurement precision can be enhanced further by optimizing the control. In some…
We study the state decay of two qubits interacted with a common harmonic oscillator reservoir. There are both decoherence error and the error caused by the amplitude change of the superradiant state. We show that frequent $π$-phase pulses can eliminate both typpes of errors therefore protect a two-qubit odd-parity state more effectively than the frequent measurement method. This shows that the the methods using dynamical decoupling and the quantum Zeno effects actually can give rather {\em different} results when the operation frequency is finite.
Dispersive interactions of matter qubits with bright squeezed light in a high-Q cavity is studied. Numerical simulation shows that higher fidelity of operations to obtain a certain phase shift of the pulse through the dispersive light-matter interaction may be reached using bright squeezed light than that using bright coherent light.
Plasmon-mediated superradiance for molecules around metallic nanospheres was proposed ten years ago. However, its demonstration has not been achieved yet due to the experimental difficulty of positioning molecules, and the theoretical limitation to the enhanced collective rate of low excited molecules. In this Letter, we propose that the ultrafast plasmon-mediated superradiant pulses can be observed with strongly excited methylene blue molecules standing vertically inside gold nanoparticle-on-mirror nanocavities. Our simulations indicate that in this system the molecules could interact with ea…
An analytical perturbation theory of short-pulse, matter-wave superradiant scatterings is presented. We show that Bragg resonant enhancement is incapacitated and both positive and negative order scatterings contribute equally. We further show that propagation gain is small and scattering events primarily occur at the end of the condensate where the generated field has maximum strength, thereby explaining the apparent ``asymmetry" in the scattered components with respect to the condensate center. In addition, the generated field travels near the speed of light in a vacuum, resulting in signific…
In this work we demonstrate the efficacy of neural networks in the characterization of dispersive media. We also develop a neural network to make predictions for input probe pulses which propagate through a nonlinear dispersive medium, which may be applied to predicting optimal pulse shapes for a desired output. The setup requires only a single pulse for the probe, providing considerable simplification of the current method of dispersion characterization that requires frequency scanning across the entirety of the gain and absorption features. We show that the trained networks are able to predi…
We present a formalism that accounts for the evolution of quantum states of travelling light pulses incident on and emanating from a local quantum scatterer such as an atom or a cavity. We assume non-dispersive asymptotic propagation of the pulses and Markovian coupling of the stationary system to input and output fields. This permits derivation of a cascaded system master equation where the input and output pulses are treated as single oscillator modes that both couple to the local system. As examples of our theory we analyse reflection by an empty cavity with phase noise, stimulated atomic e…
We describe a system for long-distance distribution of quantum entanglement, in which coherent light with large average photon number interacts dispersively with single, far-detuned atoms or semiconductor impurities in optical cavities. Entanglement is heralded by homodyne detection using a second bright light pulse for phase reference. The use of bright pulses leads to a high success probability for the generation of entanglement, at the cost of a lower initial fidelity. This fidelity may be boosted by entanglement purification techniques, implemented with the same physical resources. The nee…
We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum (OAM) in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.
There has recently been some interest in the prospect of detecting ionized intergalactic baryons by examining the properties of incoherent light from background cosmological sources, namely quasars. Although the paper by \cite{lieu13} proposed a way forward, it was refuted by the later theoretical work of \cite{hir14} and observational study of \cite{hal16}. In this paper we investigated in detail the manner in which incoherent radiation passes through a dispersive medium both from the frameworks of classical and quantum electrodynamics, which led us to conclude that the premise of \cite{lieu1…
In the propagation of optical pulses through dispersive media, the frequency degree of freedom acts as an effective decohering environment on the polarization state of the pulse. Here we discuss the application of open-loop dynamical-decoupling techniques for suppressing such a polarization decoherence in one-way communication channels. We describe in detail the experimental proof of principle of the "bang-bang" protection technique recently applied to flying qubits in [Damodarakurup et al., Phys. Rev. Lett. 103, 040502]. Bang-bang operations are implemented through appropriately oriented wave…
Intense, well-controlled regular light pulse trains start to play a crucial role in many fields of physics. We theoretically demonstrate a very simple and robust technique for generating such periodic ultrashort pulses from a continuous probe wave which propagates in a dispersive thermal gas media.
A simple method for the production of ultrashort light pulses (USPs) with suppressed photon fluctuations is considered. The method is based on self-phase modulation (SPM) of an USP in a nonlinear medium (optical fibre) and subsequent transmission of pulse through a dispersive optical element.
The dispersion cancellation feature of pulses which are entangled in frequency is employed to synchronize clocks of distant parties. The proposed protocol is insensitive to the pulse distortion caused by transit through a dispersive medium. Since there is cancellation to all orders, also the effects of slowly fluctuating dispersive media are compensated. The experimental setup can be realized with currently available technology, at least for a proof of principle.
We present two pulse schemes for actively depleting measurement photons from a readout resonator in the nonlinear dispersive regime of circuit QED. One method uses digital feedback conditioned on the measurement outcome while the other is unconditional. In the absence of analytic forms and symmetries to exploit in this nonlinear regime, the depletion pulses are numerically optimized using the Powell method. We shorten the photon depletion time by more than six inverse resonator linewidths compared to passive depletion by waiting. We quantify the benefit by emulating an ancilla qubit performing…
We describe bichromatic superradiant pump-probe spectroscopy as a tomographic probe of the Wigner function of a dispersing particle beam. We employed this technique to characterize the quantum state of an ultracold atomic beam, derived from a Rb-87 Bose-Einstein condensate, as it propagated in a 2.5 mm diameter circular waveguide. Our measurements place an upper bound on the longitudinal phase-space area occupied by the 300,000 atom beam of 9(1) $\hbar$ and a lower bound on the coherence length (L > 13 microns). These results are consistent with full quantum degeneracy after multiple orbits ar…
