Ensemble Of Two-level Atoms Research Articles

Atom-magnon entanglement in a coupled cavity-magnon atom-optomechanical system

We propose an alternative way to realize macroscopic entanglement between an atomic ensemble and ferrimagnetic magnons in a hybrid cavity-magnon atom-optomechanics, in which a microwave cavity couples to the magnons via magnetic dipole interaction, and simultaneously couples to a standard optomechanical cavity with an ensemble of two-level atoms. We show that in experimental feasible parameters, the optomechanical entanglement can be transferred to the bipartite subsystems, which makes it possible to generate the macroscopic atom-magnon entanglement and genuine tripartite entanglement. We mainly analyze the effects of coupling strengths on the efficiency of the entanglement transfer and the generation of the atom-magnon entanglement. We find that by selecting appropriate coupling strengths, both the degree of the atom-magnon entanglement and its robustness against the environmental temperature are enhanced significantly.

Theoretical model for correlations between two symmetric Four-Wave Mixing processes in an atomic two-level system

The dependence of the correlations between two symmetric four-wave mixing (FWM) signals on detuning is discussed through a simple theoretical model. The model consists of an ensemble of two-level atoms interacting with two electric fields in the semi-classical approach. Using the density matrix formalism, stochastic equations for the component of coherence responsible for the FWM processes are obtained. Here, the stochastic nature of the problem arises from the phase of the fields. Through Ito’s calculus, the stochastic differential equations are solved and the dependence of the cross-correlation function G(2) on the detuning of one field is analyzed. The emergence of Rabi oscillations in the G(2) function, consistent with previous experimental findings, is observed. What is more, for weak detuning, there is a crossover from the correlation to the anticorrelation regime, the latter persisting for a relatively large range of detuning. This paper could be of interest for the optimization of the experimental parameters for the correlations between FWM signals.

Quantum simulation of an extended Dicke model with a magnetic solid

The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO3, where the role of atoms (photons) is played by Er3+ spins (Fe3+ magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems.

Optomechanically induced transparency in a hybrid system containing two-level atomic ensemble and optical parametric amplifier

We investigate the physical properties of multiple optomechanically induced transparency in a system. The system consists of two charged mechanical resonators and an optical cavity. An optical parametric amplifier (OPA) and a two-level atom ensemble are filled into the optical cavity. Some physical phenomena appear in the system driven by the probe field and the pump field. The width of transparent windows can be manipulated by the coupling strengths of the system. Specifically, the width of the transparency window increases with an increase in the parametric gain of the optical parametric amplifier (OPA). Furthermore, the number of transparent windows and the location of transparent points are also affected by the system parameters. The presence of two-level atomic ensemble causes the double transparent windows to be split three transparent windows. The Coulomb coupling between the two charged mechanical resonators causes the transparent points to move. Our approach provides a great flexibility for manipulating multiple induced transparency. It is helpful to study the quantum properties of nonlinear optical systems.

Observation of Superradiant Bursts in a Cascaded Quantum System

We experimentally investigate the collective radiative decay of a fully inverted ensemble of two-level atoms for a chiral, i.e., propagation direction-dependent light-matter coupling. Despite a fundamentally different interaction Hamiltonian which has a reduced symmetry compared to the standard Dicke case of superradiance, we do observe a superradiant burst of light. The burst occurs above a threshold number of atoms, and its peak power scales faster with the number of atoms than in the case of free-space Dicke superradiance. We measure the first-order coherence of the burst and experimentally distinguish two regimes, one dominated by the coherence induced during the excitation process and the other governed by vacuum fluctuations. Our results shed light on the collective radiative dynamics of cascaded quantum many-body systems, i.e., systems in which each quantum emitter is only driven by light radiated by emitters that are upstream in the cascade. Our findings may turn out useful for generating multiphoton Fock states as a resource for quantum technologies. Published by the American Physical Society 2024

Conventional and Unconventional Dicke Models: Multistabilities and Nonequilibrium Dynamics.

The Dicke model describes the collective behavior of a subwavelength-size ensemble of two-level atoms (i.e., spin-1/2) interacting identically with a single quantized radiation field of a cavity. Across a critical coupling strength it exhibits a zero-temperature phase transition from the normal state to the superradiant phase where the field is populated and the collective spin acquires a nonzero x component, which can be imagined as ferromagnetic ordering of the atomic spins along x. Here we introduce a variant of this model where two subwavelength-size ensembles of spins interact with a single quantized radiation field with different strengths. Subsequently, we restrict ourselves to a special case where the coupling strengths are opposite (which is unitarily equivalent to equal-coupling strengths). Because of the conservation of the total spin in each ensemble individually, the system supports two distinct superradiant states with x-ferromagnetic and x-ferrimagnetic spin ordering, coexisting with each other in a large parameter regime. The stability and dynamics of the system in the thermodynamic limit are examined using a semiclassical approach, which predicts nonstationary behaviors due to the multistabilities. At the end, we also perform small-scale full quantum-mechanical calculations, with results consistent with the semiclassical ones.

Fast simulation for multi-photon, atomic-ensemble quantum model of linear optical systems addressing the curse of dimensionality

Photons are elementary particles of light in quantum mechanics, whose dynamics can be difficult to gain detailed insights, especially in complex systems. Simulation is a promising tool to resolve this issue, but it must address the curse of dimensionality, namely, that the number of bases increases exponentially in the number of photons. Here we mitigate this dimensionality scaling by focusing on optical systems composed of linear optical objects, modeled as an ensemble of two-level atoms. We decompose the time evolutionary operator on multiple photons into a group of time evolution operators acting on a single photon. Since the dimension of a single-photon time evolution operator is exponentially smaller than that of a multi-photon one in the number of photons, the decomposition enables the multi-photon simulations to be performed at a much lower computational cost. We apply this method to basic single- and multi-photon phenomena, such as Hong–Ou–Mandel interference and violation of the Bell-CHSH inequality, and confirm that the calculated properties are quantitatively comparable to the experimental results. Furthermore, our method visualizes the spatial propagation of photons hence provides insights that aid experiment designs for quantum-enabled technologies.

Nonreciprocal macroscopic tripartite entanglement in atom-optomagnomechanical system

We investigate how to generate the nonreciprocal macroscopic tripartite entanglement among the atomic ensemble, ferrimagnetic magnon and mechanical oscillator in a hybrid atom-optomagnomechanical system, where an ensemble of two-level atoms and a yttrium iron garnet micro-bridge supporting the magnon and mechanical modes are placed in a spinning optical resonator driven by a laser field. The phonon being the quantum of the mechanical mode interacts with the magnon and the optical photon via magnetostriction and radiation pressure, respectively, and meanwhile the photon couples to the atomic ensemble. The results show that not only all bipartite entanglements but also the genuine tripartite entanglement among the atomic ensemble, magnon and phonon could be generated at the steady state. Moreover, the nonreciprocity of atom-magnon-phonon entanglement can be obtained with the aid of the optical Sagnac effect by spinning the resonator, in which the entanglement is present in a chosen driving direction but disappears in the other direction. The nonreciprocal macroscopic tripartite entanglement is robust against temperature and could be flexibly controlled by choosing the system parameters. Our work enriches the study of macroscopic multipartite quantum states, which may have potential applications in the development of quantum information storage and the construction of multi-node chiral quantum network.

Enhancing nonclassical correlations for light scattered by an ensemble of cold two-level atoms.

We report the enhancement of quantum correlations for biphotons generated via spontaneous four-wave mixing in an ensemble of cold two-level atoms. This enhancement is based on the filtering of the Rayleigh linear component of the spectrum of the two emitted photons, favoring the quantum-correlated sidebands reaching the detectors. We provide direct measurements of the unfiltered spectrum presenting its usual triplet structure, with Rayleigh central components accompanied by two peaks symmetrically located at the detuning of the excitation laser with respect to the atomic resonance. The filtering of the central component results in a violation of the Cauchy-Schwarz inequality to (4.8±1.0)≰1 for a detuning of 60 times the atomic linewidth, representing an enhancement by a factor of four compared with the unfiltered quantum correlations observed at the same conditions.

Quantum battery based on dipole-dipole interaction and external driving field.

The Dicke model is a fundamental model in quantum optics, which describes the interaction between quantum cavity field and a large ensemble of two-level atoms. In this work, we propose an efficient charging quantum battery achieved by considering an extension Dicke model with dipole-dipole interaction and an external driving field. We focus on the influence of the atomic interaction and the driving field on the performance of the quantum battery during the charging process and find that the maximum stored energy exhibits a critical phenomenon. The maximum stored energy and maximum charging power are investigated by varying the number of atoms. When the coupling between atoms and cavity is not very strong, compared to the Dicke quantum battery, such quantum battery can achieve more stable and faster charging. In addition, the maximum charging power approximately satisfies a superlinear scaling relation P_{max}∝βN^{α}, where the quantum advantage α=1.6 can be reached via optimizing the parameters.

Quantum multicritical behavior for coupled optical cavities with driven laser fields

Quantum phase transitions with multicritical points are fascinating phenomena occurring in interacting quantum many-body systems. However, multicritical points predicted by theory have been rarely verified experimentally; finding multicritical points with specific behaviors and realizing their control remains a challenging topic. Here, we propose a system that a quantized light field interacts with a two-level atomic ensemble coupled by microwave fields in optical cavities, which is described by a generalized Dicke model. Multicritical points for the superradiant quantum phase transition are shown to occur. We determine the number and position of these critical points and demonstrate that they can be effectively manipulated through the tuning of system parameters. Particularly, we find that the quantum critical points can evolve into a Lifshitz point (LP) if the Rabi frequency of the light field is modulated periodically in time. Remarkably, the texture of atomic pseudo-spins can be used to characterize the quantum critical behaviors of the system. The magnetic orders of the three phases around the LP, represented by the atomic pseudo-spins, are similar to those of an axial next-nearest-neighboring Ising model. The results reported here are beneficial for unveiling intriguing physics of quantum phase transitions and pave the way towards to find novel quantum multicritical phenomena based on the generalized Dicke model.

Active whispering-gallery microclock in pulsed-operation mode

A whispering-gallery-mode microlaser in the bad-cavity limit serves as an active optical clock. In this clock scheme, an ensemble of two-level atoms is trapped in a two-color ring-shaped optical lattice, i.e., Lamb-Dicke regime, and evanescently interacts with an optical microcavity. The microclock is operated in the pulsed mode, where the atoms are periodically pumped into the upper state of the electric-dipole-forbidden clock transition, providing the optical gain. The numerical simulation shows that the fractional frequency instability of the microclock reaches $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ at ${10}^{3}$ s of averaging, mainly limited by the lattice-induced frequency shifts. This miniature optical clock owns the high integration and can be potentially used to supply the time standard in a photonic network, paving the way towards the on-chip metrology.

Pulse-area theorem in a single-mode waveguide and its application to photon echo and optical memory in Tm3+:Y3Al5O12

We derive the area theorem for light pulses interacting with an inhomogeneously broadened ensemble of two-level atoms in a single-mode optical waveguide and present its analytical solution for Gaussian-type modes, which demonstrates the significant difference from the formation of $2\ensuremath{\pi}$ pulses by plane waves. We generalize this theorem to the description of photon echo and apply it to the two-pulse (primary) echo and the revival of silenced echo (ROSE) protocol of photon echo quantum memory. We implemented ROSE protocol in a single-mode laser-written waveguide made of an optically thin crystal ${\mathrm{Tm}}^{3+}$:${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ . The experimental data obtained are satisfactorily explained by the developed theory. Finally, we discuss the obtained experimental results and possible applications of the derived pulse-area approach.

Atomic memory based on recoil-induced resonances

In this work, we perform a detailed theoretical and experimental investigation of an atomic memory based on recoil-induced resonance in cold cesium atoms. We consider the interaction of nearly degenerate pump and probe beams with an ensemble of two-level atoms. A full theoretical density matrix calculation in the extended Hilbert space of the internal and external atomic degrees of freedom allows us to obtain, from first principles, the transient and stationary responses determining the probe transmission and the forward four-wave-mixing spectra. These two signals are generated together at the same order of perturbation with respect to the intensities of pump and probe beams. Moreover, we have investigated the storage of optical information on the spatial modes of light beams in the atomic external degrees of freedom, which provided a simple interpretation for the previously reported nonvolatile character of this memory. The retrieved signals after storage reveal the equivalent role of probe transmission and four-wave mixing, as the two signals have similar amplitudes. Probe transmission and forward four-wave-mixing spectra were then experimentally measured for both continuous excitation and after storage. The experimental observations are in good agreement with the developed theory, and they open another pathway for the reversible exchange of optical information with atomic systems.

Squeezing of nonlinear spin observables by one axis twisting in the presence of decoherence: An analytical study

In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.

Ground-State Cooling of the Mechanical Resonator in an Optomechanical Cavity with Two-Level Atomic Ensemble

Ground-State Cooling of the Mechanical Resonator in an Optomechanical Cavity with Two-Level Atomic Ensemble

From superradiance to subradiance: exploring the many-body Dicke ladder.

We report a time-resolved study of collective emission in dense ensembles of two-level atoms. We compare, on the same sample, the buildup of superradiance and subradiance from the ensemble when driven by a strong laser. This allows us to measure the dynamics of the population of superradiant and subradiant states as a function of time. In particular, we demonstrate the buildup in time of subradiant states through superradiant dynamics. This illustrates the dynamics of the many-body density matrix of superradiant ensembles of two-level atoms when departing from the ideal conditions of Dicke superradiance, in which symmetry forbids the population of subradiant states.

Observation of Nonclassical Correlations in Biphotons Generated from an Ensemble of Pure Two-Level Atoms.

We report the experimental verification of nonclassical correlations for an unfiltered spontaneous four-wave mixing process in an ensemble of cold two-level atoms, confirming theoretical predictions by Du etal. in 2007 for the violation of a Cauchy-Schwarz inequality in the system, and obtaining R=(1.98±0.03)≰1. Quantum correlations are observed in a nanoseconds timescale in the interference between the central exciting frequency and sidebands dislocated by the detuning to the atomic resonance. They prevail over the noise background coming from Rayleigh scattering from the same optical transition. These correlations are fragile with respect to processes that disturb the phase of the atomic excitation, but are robust to variations in number of atoms and to increasing light intensities.

Dynamical Casimir–Polder force in a semi-infinite rectangle waveguide

In this paper, we study the dynamical Casimir–Polder force between an ensemble of identical two-level atoms and the wall of a rectangle waveguide with semi-infinite length. With the presence of both the rotating wave and counter rotating wave terms in the light–matter interaction Hamiltonian, we utilize the perturbation theory to solve the Heisenberg equation. Up to the seconder of coupling strength, we obtain the energy shift analytically and the Casimir–Polder force numerically. Our result shows that the dynamical behavior of the Casimir force is closely connected to the photon propagation in the waveguide. Therefore, we hope this work will stimulate the studies about the quantum effect in waveguide scenario.

Group delay controls of the photons transmitting through two cavities coupled by an artificial atomic ensemble: controllable electromagnetically induced transparency-like effects.

As one of the typical quantum coherence phenomena, electromagnetically induced transparency (EIT) has been extensively applied to implement various quantum coherent manipulations, typically, e.g., optical quantum memories, photonic switches, and optical quantum computations, etc. By applying the input-output theory to the photonic transports through two cavities dispersively coupled by an artificial two-level atomic ensemble, we show here that the EIT-like effects could be observed. Particularly, the transparency windows and phase shift spectra of the transmitting photons could be engineered by manipulating the atomic levels in the ensemble to adjust the effective coupling strength between the cavities. As a consequence, the group delays of the transmitting photons can be manipulated by using the EIT-like effects. The proposal is demonstrated specifically with the experimental superconducting coplanar waveguide resonators coupled by the voltage-biased electrons on liquid Helium.