Atom-field Coupling Research Articles

Collapse of superradiant phase and Dicke phase transition at finite temperature in a hybrid optical-mechanical system

In this paper, we theoretically investigate Dicke phase transition at finite temperature in a hybrid optical-mechanical system. The thermodynamic equilibrium states are presented by means of the functional path-integral approach. We plot the mean photon number of the two cavities and the corresponding phase diagram showing the effects of the coupling strength between the two cavities, the nonlinear photon-phonon interaction strength, the finite temperature, the detuning of the two cavities. The coupling strength between the two cavities can make the phase boundary of the normal phase (NP) to the superradiant phase (SP) shift left with the increase of the atom-field coupling strength. The region of the SP is suppressed completely and the SP disappears completely with the increase of the coupling strength between the two cavities or the nonlinear photon-phonon interaction strength, finally just the NP and the dynamically unstable state (DUS) exist. The nonlinear photon-phonon coupling strength just affects the turning curve, but not the phase boundary. The unstable non-zero photon number state and the SP are coexistent, similar to the optical bistability.

Switchability of multimodal optical phases in a leaky and nonlinear quantum cavity

In the present report, the question of U(1) symmetry breaking in a system of atoms and electromagnetic fields, interacting inside a leaky cavity, filled with a nonlinear medium, is addressed. In particular, the ${Z}_{2}$ discrete symmetry of the system and the emergence of optical phases are fully discussed. For the nonlinearity of a general order, with an electromagnetic field of any number of modes, conditions under which the resulting field-field interactions destroy the U(1) (and ${Z}_{2}$) symmetry are determined. We then apply the theory to the case of a collection of two-level atoms and three electromagnetic modes. Taking one of the fields as a classically adjustable pumping one, it is demonstrated that the quantized field-field coupling profoundly depends upon the pump field strength. The presence of two competing phenomena, namely, the cavity photonic dissipation and nonlinearity, is shown to lead the system towards steady behavior. The steady-state solutions to the atomic population and field quadratures exhibit the normal and superradiant phases, depending on the strengths of pumping field and atom-field couplings. The conditions for the stability of such steady-state solutions are also discussed in detail. A notable result of the present article is that by adjusting the parameters involved in the system one can switch from the normal to electric and/or magnetic superradiant phases.

Spectral properties of the singular Friedrichs–Lee Hamiltonian

We show that the Friedrichs–Lee model, which describes the one-excitation sector of a two-level atom interacting with a structured boson field, can be generalized to singular atom–field couplings. We provide a characterization of its spectrum and resonances and discuss the inverse spectral problem.

Dynamics of Entanglement and Statistical Properties in Atom-Field Interaction

In this paper, the dynamics of entanglement between a single two-level atom interacting with one-mode cavity field is investigated with zero and large detuning parameters. The von Neumann entropy and concurrence measures are used to characterize the degree of entanglement. We find that the entanglement shows the oscillating behavior which depends on the initial amplitude of the coherent field, detuning parameter, and atom-field coupling constant. Specially, we study the generation of the robust maximally entangled state and conclude that the intensity of the coherent field and detuning parameter can be utilized as the control parameters for generating robust maximally entangled state. At the end, some important statistical features such as Wigner function, Mandel parameter, and second-order correlation function will be discussed. The comparison between the entanglement and Wigner function shows that for $\chi t=(n+\frac {1}{2})\pi $ , the maximum of Wigner function has information about the entanglement between the atom and field in the Jaynes-Cummings model. Moreover, the Mandel parameter and consequently the second-order correlation function show that the radiation field has Poissonian statistics.

Stable entanglement in a quadripartite cavity optomechanics

In this paper, making use of negativity, we study bipartite entanglements in a quadripartite system composed of two two-level atoms and a cavity optomechanics. An atom is inside a single-mode cavity with a movable mirror and the other one is isolated outside, i.e., there is no direct interaction between this atom and cavity optomechanics with the atom therein. The entanglement dynamics of various types of bipartite systems obtained has been numerically investigated to understand the roles of initial state of cavity field, movable mirror and atoms, the ratio of the atom-field coupling strength to the optomechanical coupling coefficient on physical properties. The results amazingly show the bipartite entanglement between the interior and exterior isolated atoms. Depending on the above-mentioned ratio and different initial states adopted to the system, the relatively stable entanglement can be generated between the atoms. Furthermore, the so-called atomic entanglement sudden death, which is independent of the degree of entanglement of the initial state, occurs in some situations.

Manipulating the steady-state entanglement via three-level atoms in a hybrid levitated optomechanical system

We theoretically investigate the generation of steady-state entanglement in a levitated optomechanical system with a cascade three-level atomic medium and a dielectric nanosphere. There are two cavity modes, driven by two external laser beams with different frequencies, which are responsible for trapping and cooling the nanosphere. Atoms prepared in coherent superposition are injected into the cavity to manipulate the optical fields and the effective optomechanical coupling. We show that the entanglement between the nanosphere and the cavity modes can be enhanced by selecting properly the initial population of the lower atomic level. In particular, when the atoms are prepared at that level, the corresponding optomechanical entanglement increases with the increase of the atom-field coupling strength. We also investigate in detail the influence of the effective cavity field detunings, the atomic detunings, the driving power, and the nanosphere's radius and found that there exist optimal values of the effective cavity field detuning and the driving power that maximize the optomechanical entanglement. By selecting the system's parameters properly, we further demonstrate the generation of genuine tripartite entanglement between three degrees of freedom in the system. The findings here may help flexible control of the steady-state entanglement in hybrid optomechanical systems.

Resilient Mølmer-Sørensen gate with cavity QED

We propose a simple scheme for implementing resilient two-qubit entangling gates in universal cavity QED systems. The technique employs suitably designed laser pulse with modulated amplitude and phase to decrease residual qubit-cavity entanglement that reduces the fidelity of the desired entangling operation. Numerical simulations suggest that the optimized gates are robust against errors in gate time, frequency detuning, atom-field coupling constant and pulse amplitude. Moreover, the optimized gates provide increased robustness to cavity decay as well as strong suppression of atomic spontaneous emissions. With modest experimental parameters the scheme could enable a high gate fidelity exceeding 99% in realistic scenarios.

A two-photon laser in a Kerr-like medium with cross-Kerr and intensity-dependent coupling

We have studied the photon statistics of a nondegenerate two-photon laser with a medium that has both self- and cross-Kerr interactions as well as intensity-dependent atom–field coupling in the Hamiltonian. The density matrix equation of the atoms and two-mode cavity fields was derived using the standard Scully–Lamb approach and numerically solved. Under certain conditions, the photon distribution function equation was derived and solved analytically. The first few moments of photon numbers were calculated in the region above the lasing threshold. Nonclassicality of the fields was investigated by means of the Mandel Q parameter, second-order correlation functions and the Cauchy–Schwarz inequality. The results are analyzed for a range of finite Kerr parameters. Intensity-dependent coupling suppresses the nonclassicality of the field. It pushes the statistics of the field towards super-Poissonian.The self- and cross-Kerr interactions have significant roles in the nonclassicality of the two-photon cavity field and its statistics. These results are interesting for the field of quantum nonlinear optics and useful in quantum communications.

Loaded Microwave Cavity for Compact Vapor-Cell Clocks.

Vapor-cell devices based on microwave interrogation provide a stable frequency reference with a compact and robust setup. Further miniaturization must focus on optimizing the physics package, containing the microwave cavity and atomic reservoir. In this article, we present a compact cavity-cell assembly based on a dielectric-loaded cylindrical resonator. The loaded cavity resonating at 6.83 GHz has an external volume of only 35 cm3 and accommodates a vapor cell with 0.9-cm3 inner volume. The proposed design aims at strongly reducing the core of the atomic clock, maintaining, at the same time, high-performing short-term stability ( σy(τ) ≤ 5×10-13 τ-1/2 standard Allan deviation). The proposed structure is characterized in terms of microwave field uniformity and atom-field coupling with the aid of finite-element calculations. The thermal sensitivity is also analyzed and experimentally characterized. We present preliminary spectroscopy results by integrating the compact cavity within a rubidium clock setup based on the pulsed optically pumping technique. The obtained clock signals are compatible with the targeted performances. The loaded-cavity approach is, thus, a viable design option for miniaturized microwave clocks.

Bifurcations, time-series analysis of observables, and network properties in a tripartite quantum system

In a tripartite system comprising a Λ-atom interacting with two radiation fields in the presence of field nonlinearities and an intensity-dependent field-atom coupling, striking features have been shown to occur in the dynamics of the mean photon number 〈Ni(t)〉 (i=1,2) corresponding to either field. In this Letter, we carry out a detailed time-series analysis and establish an interesting correlation between the short-time and long-time dynamics of 〈Ni(t)〉. Lyapunov exponents, return maps, recurrence plots, recurrence-time statistics, as well as the clustering coefficient and the transitivity of networks constructed from the time series, are studied as functions of the intensity parameter κ. These are shown to carry signatures of a special value κ=κ‾. Our work also exhibits how techniques from nonlinear dynamics help analyze the behavior of observables in multipartite quantum systems.

Nonclassical properties and entanglement generation in an optical cavity containing two atomic Bose–Einstein condensates

We consider the model of a weakly driven optical cavity containing two clouds of atomic Bose–Einstein condensates (BECs). Nonclassical photon correlations and correlations between the two atomic BECs are investigated under different cavity conditions including strong atom-field coupling and bad cavity regime. We show that the nonlinear interatom collisional interactions in BEC leads to a significant loss of cavity light coherence. Various types of nonclassical properties are investigated such as sub-Poissonian statistics, antibunching and entanglement. We show that the entanglement can be generated between BECs and the cavity field. The time evolution of entanglement is also numerically studied.

Quantum Squeezing of the Field of a Single-Atom Laser under Conditions of a Variable Coupling Constant

A nonstationary regime of squeezed-light generation by a single-atom laser is investigated. Dependences of the quantum-squeezing parameter and radiation intensity on modulation frequency of the atom–field coupling constant are obtained. It is demonstrated that a resonance appears at the modulation frequency equal to twice the average coupling constant, which leads to a more efficient quantum squeezing in a nonstationary harmonic regime than in the case of a stationary regime for the same values of the relaxation and pump parameters.

Spin Squeezing for Two Atoms in an Optical Coherent-State Cavity

We in this paper investigate the spin squeezing in relation with the phase transition from the normal to superradiant phases for two atoms in an optical cavity. The squeezing vanishes in the normal phase and jumps sharply to the maximum bound above the critical point of phase transition. In the high atom-field coupling regime, the squeezing vanishes again when the atom-field coupling reaches a threshold value. The squeezing alternates between two spin components in the intermediate region of atom-field coupling. An interesting observation is that the two spin components are squeezed alternately with the variation of phase angle of the cavity field. The squeezing factor indeed can be used to probe the phase transition and coherent-field properties as well.

Dynamics of two dipole-coupled superconducting qubits interacting with two independent cavity modes

In this paper, we have investigated the entanglement dynamics between two dipole-coupled superconducting qubits not resonantly interacting with two microwave modes of independent coplanar resonators. The case of different atom-field couplings has been under consideration. Using the dressed-states technique we have derived the exact solution of the evolution equation for separable initial qubits states and field modes in the vacuum states. On its basis the negativity as a measure of qubit-qubit entanglement has been calculated. The time dependence of negativity for different values of detuning between the qubits and fields frequencies, atom-field couplings and strength of the dipole-dipole interaction has been investigated for different separable initial qubits states.

Electro-optomechanical switch via tunable bistability and four-wave mixing

We investigate the tunable bistable behavior of a hybrid nano-electro-optomechanical system (NEOMS) composed of S-shaped in the presence of two-level atoms, trapped inside a Fabry–Pérot cavity, and driven by a strong driving field and a weak probe field. The bistable behavior of the steady-state photon number and the mechanical steady-state positions are discussed. Further, we tune bistability by tuning all the coupling frequencies involved in the system and amplitude of the driving field. The present study provides the possibility of realization of a controllable optical switch depending on atom-field coupling, optomechanical coupling, electrostatic Coulomb coupling, and threshold power. In addition, we discuss that the non-linear effect of the hybrid NEOMS generates the four-wave mixing (FWM) process. Moreover, we show that the FWM process can be suppressed by the atom-field detuning and cavity-field detuning, which exhibits low photon transmission.

Squeezing‐Enhanced Atom–Cavity Interaction in Coupled Cavities with High Dissipation Rates

AbstractThe realization of the strong coupling regime is requisite for implementing quantum information tasks. Here, a method for enhancing the atom–field coupling in highly dissipative coupled cavities is proposed. By introducing parametric squeezing into the primary cavity, which is only virtually excited under specific parametric conditions, coupling enhancement between the atom and the auxiliary cavity is realized for appropriate squeezing parameters. This enables the system to be robust against large cavity decay and atomic spontaneous emission. The observation of vacuum Rabi oscillations show that the originally weakly coupled system can be enhanced into an effective strong coupling regime.

Optical spectroscopy of the 5p3/2 → 6p1/2 electric dipole-forbidden transition in atomic rubidium

We present the first evidence of excitation of the electric dipole-forbidden transition in atomic rubidium. The experiments were done in a rubidium vapor cell using Doppler-free optical–optical double resonance spectroscopy with counter-propagating beams, with a similar scheme to the excitation of the other fine transition 6p3/2 in the 6pJ manifold reported in Ponciano-Ojeda et al (2015 Phys. Rev. A 92 042511). The dipole-forbidden excitation occurs at a wavelength λ ≈ 917.5 nm. The spectra showed the two main hyperfine states of the 6p1/2 manifold, and also resolved up to three satellites that appear due to effects of selection of velocities in thermal rubidium atoms. The polarization dependence of the relative intensities of the hyperfine lines of the decay fluorescence is also investigated. The data show that the individual line intensities and also the total cross-section have a strong dependence on the polarization direction. Experimental data for different polarization configurations of the light beams used in this two-photon spectroscopy are compared with the results of calculations that consider a strong atom-field coupling in the preparation step, followed by a weak electric quadrupole excitation and the blue fluorescence decay emission. Good agreement between experiment and this three-step model is found in the case of linear–linear polarizations, which confirms the results found for the forbidden transition. The results presented here complete the information about the 5p3/2 → 6pJ electric dipole-forbidden transition in rubidium.

Analytical model of the single emitter laser with modulated coupling constant

Using the master equation for the density operator of the laser field, we constructed an analytic model of a single emitter laser under a strong atom-field coupling in the non-stationary regime, that is obtained by coupling constant modulation at the defined frequency. The model demonstrated the emergence of a harmonic force, that partially compensates for relaxation processes in the quantum system. The mechanism of force occurrence, is described by changing the coupling constant.

Multiple stable states and Dicke phase transition for two atoms in an optical cavity

We study in the present paper the multiple stable states of two different atoms in a single-mode quantum cavity by means of variational method. Eigenenergies and eigenstates are obtained analytically in the optical coherent state of cavity field. The ground state displays the known Dicke phase transition from the normal to superradiant phases at the critical value of atom–field coupling. The rich phase diagrams including the stable excited states are presented respectively for two atoms with different level spaces and atom–field couplings. By adjusting the ratios of two-atom couplings or level spaces, one atom can be in the normally populated state, while the other is in the inversely populated state. We also observe the stimulated radiation from the inversely populated state. Particularly, the normal and stimulated radiations are interchangeable respectively for two atoms. Moreover, the maximally entangled state can be generated with two identical atoms.

Multiphoton Jaynes-Cummings Model: Arbitrary Rotations in Fock Space and Quantum Filters.

The multiphoton Jaynes-Cummings model is investigated and applications in quantum information science are explored. Considering the strong atom-field coupling regime and an N-photon interaction, a nonlinear driving field can perform an arbitrary rotation in the Fock space of a bosonic mode involving the vacuum and an M-Fock state, with M<N. In addition, driving a bosonic mode with a linear coherent field (superposition of many Fock states), only the cavity states within the Fock subspace {|0⟩,|1⟩,…,|N-1⟩} can be populated; i.e., we show how to implement a Fock state filter, or quantum scissor, that restricts the dynamics of a given bosonic mode to a limited Hilbert space. Such a device can be employed as a generator of finite-dimensional quantum-optical states and also as a quantum-optical intensity limiter, allowing as a special case the generation of single-photon pulses. On the other hand, our system also provides a very rich physics in the weak atom-field coupling regime, in particular, multiphoton electromagnetically induced transparencylike phenomena, inducing a narrow (controllable) reflectivity window for nonlinear probe fields. These results are useful for applications in quantum information processing and also motivate further investigations, e.g., the use of an N-photon Jaynes-Cummings system as a qudit with harmonic spectrum and the exploration of multiphoton quantum interference.