Single-mode Quantized Field Research Articles

Quantum Fisher information of a $\Diamond$-type four level atom interacting with a single-mode quantized field in an optomechanical cavity

Abstract In science and technology, precision measurement of physical quantities is crucial, and the quantum Fisher information (QFI) plays a significant role in the study of quantum systems. In this work, we explore the dynamics of QFI for a hybrid optomechanical system, which consists of a $\Diamond$-type four level atom interacting with a single-mode quantized field through multi-photon process. We account for various sources of dissipation, including the decay rates of the atom, the cavity, and the mechanical modes. Using an effective Hamiltonian, we analytically derive the explicit form of the state vector of the entire system via the time-dependent Schr"{o}dinger equation. We then investigate the atomic QFI for the estimation precision of the decay rate of the mechanical oscillator. Furthermore, we examine how optomechanical and atom-field coupling strengths, dissipation parameters, and multi-photon transition influence the dynamics of atomic QFI. Our numerical results suggest that the estimation precision of the decay rate of the mechanical oscillator can be controlled by these parameters.

Response of two-band systems to single-mode quantized field with momentum

As a new quantum state, topological insulators have become the focus of condensed matter and material science. The open system research of topological insulators has aroused the interest of many researchers. In this paper, we study the response of topological insulators to a single-mode quantized field with momentum. We solve the ground state of the system after the addition of a single-mode light field with adjustable photon momentum. To be specific, the analytical solution of Hall conductance has an additional correction compared with the closed system, and the Hall conductance can no longer be expressed by the weighted sum of the Chern numbers. Furthermore, the topological properties are analyzed and discussed through the results of an instance with their illustration. The system still has a topological phase transition and the critical point of the topological phase is robust to the single-mode quantized field.

Entanglement dynamics and population inversion of a two-qubit system in two cavities coupled with optical fiber in the presence of two-photon transition

In this paper, the entanglement between two qubits that exist in two distinct cavities which are connected by an optical fiber is investigated by using the concurrence, while two-photon transitions and Kerr medium effect are also considered. Each cavity contains a qubit and a single-mode quantized field. The appearance of entanglement between the two qubits in the separate cavities originates from the presence of optical fiber. The obtained numerical results of the considered system show that, if the Kerr medium is large enough, the initial values of entanglement between the two qubits (which may have the maximum possible value, i.e. 1) can be approximately protected from the large amplitude fluctuations, so that acceptable stability is created. Also, qubit-field coupling and detuning effects are investigated and it is observed that symmetric coupling results in more stability of entanglement. Eventually, atomic population inversion is also studied and it is observed that it is controllable by considering different parameters.

Teleportation of unknown states of a qubit and a single-mode field in strong coupling regime without Bell-state measurement

In this paper, we develop the teleportation scheme in [Zheng in Phys Rev A 69, 064302, 2004], in the sense that, we work in the strong atom-field coupling regime wherein the rotating wave approximation (RWA) is no longer valid. To achieve the purpose, a scheme consisting of a qubit interacting with a single-mode quantized field is described via the Rabi model (counter rotation terms are taken into account). Our first aim is to teleport an unknown atomic state of a qubit (which interacts with the quantized field in a cavity) to a second qubit (exists in another distant cavity field), beyond the RWA and without the Bell-state measurement method. In the continuation, in a similar way, we teleport an unknown state of a single-mode field too. In fact, it is shown that, in this regime, after applying some particular conditions, containing the interaction time of atom-field in the cavities, adjusting the involved frequencies, as well as the atom-field coupling in the model, if a proper measurement is performed on the state of the first qubit (the related field in the cavity), the unknown states of the qubit (field) can be teleported from the first qubit (cavity field) to the second qubit (cavity field), appropriately. We show that in both considered cases, the teleportation protocol is successfully performed with the maximum possible fidelity, 1, and the acceptable success probability, 0.25.

Nonclassical correlations in lossy cavity optomechanics with intensity-dependent coupling

In this paper, we describe a double-optomechanical system which contains two lossy cavities, where each cavity includes a single-mode quantized field coupled to a single vibrational mode of a flexible membrane. There exists an interaction between a two-level atom and the cavity mode in the rotating wave approximation, with degenerate multi-photon transition in the presence of intensity-dependent coupling. Furthermore, we consider the effect of different sources of dissipation consisting of cavity decay, losses of cavity mirror, and spontaneous emission from the atom. We then start with the master equation to study the dynamics of considered quantum system. Afterward, we show that under some circumstances, the solution of the complicated problem via the master equation is reduced to the determination of the state vector in the time-dependent Schrödinger equation, with the help of an effective non-Hermitian Hamiltonian. Obtaining the explicit form of the state vector of the entire system, we study the nonclassical correlations of two atoms by means of geometric discord. We also examine the roles of intensity-dependent nonlinearity function, number of photons contributed to atomic transition, number of photons in the Fock states, and different sources of dissipation in the dynamics of geometric discord of the atoms. The numerical results indicate that the steady-state value of geometric discord can be revealed, and can appropriately be controlled via the mentioned-above effects. It can be found that the existence of spontaneous emission not only protects the nonclassical correlations of the atoms but also tends the geometric discord to a steady-state value.

Quantum-optical excitations of semiconductor nanostructures in a microcavity using a two-band model and a single-mode quantum field

We theoretically study quantum-optical properties of one- and two-dimensional semiconductor nanostructures, where the electronic band structure is described by a two-band tight-binding model. Since the focus of our work is on analyzing quantum-optical effects of systems with a continuous band structure, many-body processes like electron-electron and electron-phonon interactions are neglected. The quantum-optical interband excitations are fully incorporated and described by a Jaynes-Cummings-type model. The exciting quantum light can be a state with arbitrary photon statistics. For simplicity, the results discussed here are limited to single-photon and two-photon Fock states. Our analytical approach is based on the eigenvalue problem and can be utilized to obtain explicit expressions for the steady-state properties of the system. Numerical simulations are based on solutions of the equations of motion and allow for a more precise analysis of the dynamics and nonresonant excitations of the system. We demonstrate that during the interaction process, a collective excitation of the conduction band is formed. For nonresonant excitations, this collective dynamics results in interesting steady states, in which the resonantly addressed eigenstates are occupied. The presented model provides a framework for microscopic simulations of quantum-optically excited extended semiconductor nanostructures.

Quantized fields induced topological features in Harper-Hofstadter model

Classical magnetic fields might change the properties of topological insulators such as the time reversal symmetry protected topological edge states. This poses a question that whether quantized fields would change differently the feature of topological materials with respect to the classical one. In this paper, we propose a model to describe topological insulators (ultracold atoms in square optical lattices with magnetic field) coupled to a tunable single-mode quantized field, and discuss the topological features of the system. We find that the quantized field can induce topological quantum phase transitions in a different way. To be specific, for fixed gauge magnetic flux ratio, we calculate the energy bands for different coupling constants between the systems and the fields in both open and periodic boundary conditions. We find that the Hofstadter butterfly graph is divided into a pair for continuous gauge magnetic flux ratio, which is different from the one without single-mode quantized field. In addition, we plot topological phase diagrams characterized by Chern number as a function of the momentum of the single-mode quantized field and obtain a quantized structure with non-zero filling factor.

Eigenstates of two-level systems in a single-mode quantum field: from quantum Rabi model to N-atom Dicke model in the Coulomb gauge

In the present paper we show that the Hamiltonian describing the resonant interaction of N two-level systems with a single-mode electromagnetic quantum field in the Coulomb gauge can be diagonalized with a high degree of accuracy using a simple basis set of states. This allows one to find an analytical approximation for the eigenvectors and eigenvalues of the system, which interpolates the numerical solution in a broad range of the coupling constant values. For the first time, we show that the energy spectrum of Dicke model (DM) as a function of N (with ) satisfies the simple scaling relation. In addition, the introduced basis states provide a regular way of calculating the corrections and estimating the convergence to the exact numerical solution. Analytical approximations and numerical results describing the energy spectrum are valid for both quantum Rabi model (N = 1) and DM for atoms.

F-deformed cavity mode coupled to a Λ-type atom in the presence of dissipation and Kerr nonlinearity

In this paper, the dynamics of a system consisting of a three-level atom, which interacts with a single-mode quantized field in a lossy cavity, is studied in the presence of the dependence of atom–field coupling and third-order nonlinear susceptibility on the intensity of light. The system contains a Λ -type atom coupled to a single-mode radiation field, with a degenerate multi-photon transition in the intensity-dependent regime. Also, the nonlinearity of the medium due to Kerr and intensity-dependent Kerr effects, and the detuning parameters are considered. Furthermore, to see the effects of dissipation such as photon absorption and scattering by the cavity mirrors and spontaneous emission of the atom, a non-Hermitian Hamiltonian is introduced, which results in obtaining the state vector of the whole system by applying the time-dependent Schrödinger equation. Thereupon, the dynamics of entanglement, coherence, photon statistics, and quadrature squeezing are numerically investigated. In each case, the roles of the intensity-dependent nonlinearity function, Kerr and intensity-dependent Kerr nonlinearity, different sources of dissipation, and detuning parameters are discussed. The numerical results indicate that the nonclassicality can remarkably be revealed, and can appropriately be controlled via the above-mentioned effects. It can be found that the presence of dissipation not only does not weaken the physical properties but also can enhance and protect the nonclassicality of the system.

Radiation-induced interaction potential of two qubits strongly coupled with a quantized electromagnetic field

We investigate the interaction of two two-level qubits with a single mode quantum field in a cavity without rotating wave approximation and considering that qubits can be located at an arbitrary distance from each other. We demonstrate that there exists a radiation induced interaction potential between atoms. We studied the properties of the system numerically and in addition constructed a simple analytical approximation. It is shown that the observable characteristics are substantially dependent on the distance between the qubits in the strong coupling regime. This allows one to perform the quantum control of the qubits, which can be exploited for the recording and transmission of quantum information.

The amplitude of the cavity pump field and dissipation effects on the entanglement dynamics and statistical properties of an optomechanical system

In this paper we consider a cavity optomechanics consists of a two-level atom that interacts with a single-mode quantized field in the presence of a strong driving laser. By evaluating the effective Hamiltonian of the whole system which contains the field dissipation, we derive the time-dependent state vector of the system corresponding to particular initial conditions for the cavity field and oscillatory mirror. In the continuation, we pay our attention to the dynamical properties of the considered system by choosing different initial conditions for the atom. In particular, the effects of amplitude of the pump field, various initial atomic states and cavity loss rate on the entanglement, atomic population inversion and photon and phonon statistical properties are numerically analysed. According to the obtained results, maximal entanglement for all chosen initial states of the system is visible as time develops. Moreover, the presence of dissipative field leads to decrease the entanglement and finally tends to a fixed positive value, while the Mandel parameter as well as the population inversion reduce and tend to a fixed value in the negative region. Also, the appearance of non-classicality feature such as typical collapse–revival phenomenon in the (negative values of) Mandel parameter is noticeable.

Dynamic Properties for BEC in an Optical Cavity with Atom-Photon Nonlinear Interaction

In this paper we investigate the dynamics of physical properties of the system introduced in Dimer et al. (Phys. Rev. A 75, 013804, 2007) and Zhao et al. (Phys. Rev. A 90, 023622, 2014) consisting of an ensemble of four-level atoms in Bose-Einstein condensate (BEC) state and a single-mode quantized field in which nonlinear interaction is taken into account. In fact, we start with a four-level atom and then explain how this model can be reduced to an effective two-level one via the adiabatic elimination. Also, our presentation is free of any classical approximation and so it is fully quantized. In this regard, we introduce the dynamical Hamiltonian of the system in terms of angular momentum operators and use the Dicke model to achieve the state of atomic sub-system. After obtaining the analytical solution of the state vector associated with the quantized BEC-field system, various physical properties such as atomic population inversion, quantum statistics of the field, squeezing in atomic and field subsystems as well as the degree of entanglement between the “BEC atoms” and the “photons” are numerically evaluated. It is shown that, the nonlinear interaction and other involved parameters in the presented model can dramatically affect the dynamics of the system. The collapse-revival phenomenon in the population inversion, Mandel parameter and atomic squeezing is a superb feature of the system which can be controlled by tuning the chosen parameters. Meanwhile, we propose an efficient way for the generation of sub-Poissonian and squeezed fields as well as squeezed atoms via nonlinear interaction of quantized filed with atomic BEC. In addition, it is found that, after the onset of interaction the system is always entangled. Altogether, under particular conditions, the approximated sudden death and then revival of entanglement can be observed.

Interaction of broadband quantum fields with resonant atoms in second-order algebraic perturbation theory

The second-order algebraic perturbation theory provides a correct and conventional description of the interaction of a single-mode quantized field and a broadband field with resonant particles, and in case of interacting two different broadband fields in the Markov approximation the generalization of the Hudson-Parthasarathy algebra is required to derive the Schrödinger equation.

Optically tunable spin texture of the surface state for Bi2Se3 and SmB6 topological insulators.

The spin texture of the surface state for topological insulators can be manipulated by the polarization of light, which might play a potential role in the applications in spintronics. However, the study so far in this direction mainly focuses on the classical light-topological-insulators interactions; TIs coupled to quantized light remains barely explored. In this paper, we develop a formalism to deal with this issue of spin texture of the surface state for topological insulators (for example Bi2Se3 and SmB6) irradiated by a quantum field, and we find that the coupling between an electron and a single-mode quantum field modulates only the arrow length that represents the spin polarization of a topological surface state. Specifically, when the photon number of a single-mode quantum field is fixed, the azimuth angle between the quantum light and the material surface manipulates the spin textures along the constant energy contour rotating (clockwise or counterclockwise) around the high symmetry point, and the polar angle controls the magnitude of the spin polarization. These results are quite different from the situation where an external field is not applied to an electron in a crystal or where a classical external field is utilized to control the spin polarization of a photoemitted electron in a vacuum. Our results have potential applications in quantum optics and condensed-matter physics.

Spontaneous Emission Originating from Atomic BEC Interacting with a Single-Mode Quantized Field

In this paper we present a general theoretical model for the interaction between a number of two-level atoms constituting Bose-Einstein condensate (BEC) and a single-mode quantized field. In addition to the usual interacting terms, we take into account interatom as well as higher-order atom-field interactions. To simplify the Hamiltonian of system, after using the Bogoliubov approximation we proceed to calculate the transformed operators of atoms and field. Then, to quantify the spontaneous emission, we get analytical expressions for the expectation value of as the atomic population inversion (API), in the cases of number and coherent states for the atomic subsystem. Our results show that the above-mentioned model interaction leads to the appearance of collapse-revival phenomenon in API. In more detail, the revival time may be tuned by adjusting the interatom interaction constant. Also, the damping process lowers the amplitude of API, but does not change the CR times for weak damping. Moreover, increasing the damping may decrease the number of CRs in a given interval of time such that no revival occurs. Briefly, it may be concluded that in the resonant case the revival times are insensitive to the change of the higher-order atom-field interaction constant and are affected only by the interatom interactions. Finally, we express that, how we can find a practical procedure to measure the quantum states of atoms in BEC.

Collapse and revival of entanglement between qubits coupled to a spin coherent state

We extend the study of the Jayne–Cummings (JC) model involving a pair of identical two-level atoms (or qubits) interacting with a single mode quantized field. We investigate the effects of replacing the radiation field mode with a composite spin, comprising [Formula: see text] qubits, or spin-1/2 particles. This model is relevant for physical implementations in superconducting circuit QED, ion trap and molecular systems. For the case of the composite spin prepared in a spin coherent state, we demonstrate the similarities of this set-up to the qubits-field model in terms of the time evolution, attractor states and in particular the collapse and revival of the entanglement between the two qubits. We extend our analysis by taking into account an effect due to qubit imperfections. We consider a difference (or “mismatch”) in the dipole interaction strengths of the two qubits, for both the field mode and composite spin cases. To address decoherence due to this mismatch, we then average over this coupling strength difference with distributions of varying width. We demonstrate in both the field mode and the composite spin scenarios that increasing the width of the “error” distribution increases suppression of the coherent dynamics of the coupled system, including the collapse and revival of the entanglement between the qubits.

Stability of various entanglements in the interaction between two two-level atoms with a quantized field under the influences of several decay sources

In this paper the interaction between two two-level atoms with a single-mode quantized field is studied. To achieve exact information about the physical properties of the system, one should take into account various sources of dissipation such as photon leakage of cavity, spontaneous emission rate of atoms, internal thermal radiation of cavity and dipole–dipole interaction between the two atoms. In order to achieve the desired goals, we obtain the time evolution of the associated density operator by solving the time-dependent Lindblad equation corresponding to the system. Then, we evaluate the temporal behavior of total population inversion and quantum entanglement between the evolved subsystems, numerically. We clearly show that how the damping parameters affect on the dynamics of considered properties. By analyzing the numerical results, we observe that increasing each of the damping sources leads to faster decay of total population inversion. Also, it is observed that, after starting the interaction, the entanglement between one atom with other parts of the system as well as the entanglement between “atom–atom” subsystem and the “field”, tend to some constant values very soon. Moreover, the stable values of entanglement are reduced via increasing the damping factor $$\varGamma _{\mathrm{A}}$$ ( $$\varGamma _{\mathrm{A}}^{(1)} = \varGamma _{\mathrm{A}}^{(2)} = \varGamma _{\mathrm{A}}$$ ) where $$\varGamma _{\mathrm{A}}$$ is the spontaneous emission rate of each atom. In addition, we find that by increasing the thermal photons, the entropies (entanglements) tend sooner to some increased stable values. Accordingly, we study the atom–atom entanglement by evaluating the concurrence under the influence of dissipation sources, too. At last, the effects of dissipation sources on the genuine tripartite entanglement between the three subsystems include of two two-level atoms and a quantized field are numerically studied. Due to the important role of stationary entanglement in quantum information processing, our results may provide useful hints for practical protocols which require some appropriate mechanisms to prevent or at least minimize the influence of decoherence phenomenon.

Entanglement Dynamics of Linear and Nonlinear Interaction of Two Two-Level Atoms with a Quantized Phase-Damped Field in the Dispersive Regime

In this paper we study the linear and nonlinear (intensity-dependent) interactions of two two-level atoms with a single-mode quantized field far from resonance, while the phase-damping effect is also taken into account. To find the analytical solution of the atom-field state vector corresponding to the considered model, after deducing the effective Hamiltonian we evaluate the time-dependent elements of the density operator using the master equation approach and superoperator method. Consequently, we are able to study the influences of the special nonlinearity function $f (n) = \sqrt {n}$ , the intensity of the initial coherent state field and the phase-damping parameter on the degree of entanglement of the whole system as well as the field and atom. It is shown that in the presence of damping, by passing time, the amount of entanglement of each subsystem with the rest of system, asymptotically reaches to its stationary and maximum value. Also, the nonlinear interaction does not have any effect on the entanglement of one of the atoms with the rest of system, but it changes the amplitude and time period of entanglement oscillations of the field and the other atom. Moreover, this may cause that, the degree of entanglement which may be low (high) at some moments of time becomes high (low) by entering the intensity-dependent function in the atom-field coupling.

Quantum dynamics of a BEC interacting with a single-mode quantized field under the influence of a dissipation process: thermal and squeezed vacuum reservoirs

In this paper we consider a system consisting of a number of two-level atoms in a Bose–Einstein condensate (BEC) and a single-mode quantized field, which interact with each other in the presence of two different damping sources, i.e. cavity and atomic reservoirs. The reservoirs which we consider here are thermal and squeezed vacuum ones corresponding to field and atom modes. Strictly speaking, by considering both types of reservoirs for each of the atom and field modes, we investigate the quantum dynamics of the interacting bosons in the system. Then, via solving the quantum Langevin equations for such a dissipative BEC system, we obtain analytical expressions for the time dependence of atomic population inversion, mean atom as well as photon number and quadrature squeezing in the field and atom modes. Our investigations demonstrate that for modeling the real physical systems, considering the dissipation effects is essential. Also, numerical calculations which are presented show that the atomic population inversion, the mean number of atoms in the BEC and the photons in the cavity possess damped oscillatory behavior due to the presence of reservoirs. In addition, non-classical squeezing effects in the field quadrature can be observed especially when squeezed vacuum reservoirs are taken into account. As an outstanding property of this model, we may refer to the fact that one can extract the atom–field coupling constant from the frequency of oscillations in the mentioned quantities such as atomic population inversion.

Decoherence in quantum lossy systems: superoperator and matrix techniques

Due to the unavoidably dissipative interaction between quantum systems with their environments, the decoherence flows inevitably into the systems. Therefore, to achieve a better understanding on how decoherence affects on the damped systems, a fundamental investigation of master equation seems to be required. In this regard, finding out the missed information which has been lost due to irreversibly of the dissipative systems, is also of practical importance in quantum information science. Motivating by these facts, in this work we want to use superoperator and matrix techniques, by which we are able to illustrate two methods to obtain the explicit form of density operators corresponding to damped systems at arbitrary temperature T ≥ 0. To establish the potential abilities of the suggested methods, we apply them to deduce the density operator of some practical well-known quantum systems. Using the superoperator techniques, at first we obtain the density operator of a damped system which includes a qubit interacting with a single-mode quantized field within an optical cavity. As the second system, we study the decoherence of a quantized field within an optical damped cavity. We also use our proposed matrix method to study the decoherence of a system which includes two qubits in the interaction with each other via dipole-dipole interaction and at the same time with a quantized field in a lossy cavity. The influences of dissipation on the decoherence of dynamical properties of these systems are also numerically investigated. At last, the advantages of the proposed superoperator techniques in comparison with matrix method are explained.