Lossless Cavity Research Articles

Dynamics for a two-atom two-mode intensity-dependent Raman coupled model

We study the quantum dynamics of a two-atom Raman coupled model interacting with a quantized bimodal field with intensity-dependent coupling terms in a lossless cavity. The unitary transformation method used to solve the time-dependent problem also gives the eigensolutions of the interaction Hamiltonian. We study the atomic-population dynamics and dynamics of the photon statistics in the two cavity modes, and present evidence of cooperative effects in the production of antibunching and anticorrelations between the modes. We also investigate the effect of detuning on the evolution of second-order correlation functions and observe that the oscillations become more rapid for large detuning.

Control of atom-atom entanglement by cavity detuning

Using the atomic levels previously employed to demonstrate a two-photon maser, we show that the atom-atom entanglement produced by the successive passage of two three-level Rydberg atoms across a single-mode lossless cavity can be enhanced using the Stark shift. The atoms are assumed to be prepared in their excited states and to interact with the field during the same amount of time. Employing a physically motivated perturbation-theory approach, we obtain an effective two-level Hamiltonian. We show that, within the limits of validity of the approximation, atomic entanglement can be controlled by changing the frequency of the cavity field, and can be enhanced up to a maximum where the squared concurrence attains the value 16/27.

Generation of Atomic-Squeezed States via Pondermotively Squeezed Light

We study the generation of atomic-squeezed states for a Bose-Einstein Condensate confined within the lossless optomechanical cavity using pondermotively squeezed light. We show that the radiation pressure coupling between the optical cavity field and mechanical motion of the cavity end mirror generates squeezing of light. This radiation pressure induced light squeezing gets transferred to the condensate atoms via Tavis-Cummings type interaction and results in squeezed-spin states. We further discuss the effect of optomechanical coupling on squeezed atomic states.

Effect of optomechanical coupling on squeezed-spin states

We investigate the effect of optomechanical coupling on the squeezed-spin states for a Bose-Einstein Condensate embedded within the lossless optomechanical cavity for the three special cases of initial states of cavity field, namely, a coherent state, a squeezed vacuum state and a squeezed state. We show that the radiation pressure or pondermotive force acting on the cavity end mirror plays a significant role in producing the atomic-squeezed states by producing squeezed states of the cavity field which is then transferred to the condensate. We further show that the maximum spin-squeezing along the x-direction is obtained in the presence of optomechanical coupling for the initial cavity field prepared in the amplitude squeezed state, whereas, squeezing along the y-direction reaches a maximum value in the absence of optomechanical coupling for the initial coherent cavity field. We also study the additional effect of nonlinear atomic interaction on spin-squeezing.

DYNAMICS OF TWO-LEVEL ATOMS INTERACTING WITH THERMAL FIELD FOR ENTANGLED INITIAL ATOMIC STATES

In this paper the entanglement dynamics for system of two two-level atoms interacting with a mode of thermal electromagnetic field in lossless cavity has been investigated. Initial atomic states are the entangled Bell type states. Using the full set of eigenvectors of the Hamiltonian of the considered model we have derived the exact solution for the density matrix for the whole system. On its basis the reduced atomic density matrix and Peres - Horodetcki parameter have been calculated. Calculating of entanglement parameter shows the possibility of high degree of entanglement even for large intensity of thermal field. Thus there is a possibility of maintenance and control over the degree of entanglement.

Thermal atom–atom entanglement in a nonlinear cavity

In the present report thermal entanglement between two-coupled two-level atoms as two identical qubits inside a single mode lossless cavity, filled with a centrosymmetric medium, is investigated. In the presence of the centrosymmetric medium, photonic cavity mode couples with itself via the third order susceptibility. The cavity is also assumed to be in thermal equilibrium with a heat reservoir so that all atom–photon states with definite probabilities participate into the entanglement. A Casimir operator of the system, which commutes with the total Hamiltonian, indicates that the Hamiltonian representation is block-diagonal. Diagonalizing of each block, the thermal density operator, written in the bases of total Hamiltonian, is obtained. Partial tracing of thermal density matrix over the photonic states, the atomic reduced density matrix, and consequently, the concurrence, as a measure of entanglement, are determined as functions of temperature. The concurrence shows that the thermal atom–atom entanglement starts from zero at zero temperature, becomes more entangled, reaching the maximal at a critical temperature and terminates abruptly at a finite temperature. The influence of medium on the thermal atom–atom entanglement is also examined.

Entanglement Between Qubits Interacting with Thermal Field

We have investigated the entanglement between two dipole coupled two-level artificial atoms (superconducting qubits, ion, spins etc.). The model, in which only one atom is trapped in an lossless cavity and interacts with single-mode thermal field, and the other one can be spatially moved freely outside the cavity has been carried out. We have considered the effect of the atomic coherence on the entanglement behavior. We have shown that a thermal field might cause high entanglement between the atoms both for coherent and incoherent initial atomic states only for small values of cavity mean photon number. We have also derived that the degree of entanglement is weakly dependent on the strength of dipole-dipole interaction for coherent initial states. In the considered model the atoms would get entangled even when both atoms are initially in the excited state.

High temperature collective spin-photon coupling in a microwave cavity

An ensemble of N identical noninteracting spins being in thermal equilibrium and coupled to the resonant mode of a lossless microwave cavity is studied at arbitrary temperature T. Near T = 0 the system is known to be in a coupled spin-photon state that manifests itself by the splitting of the cavity mode (vacuum Rabi splitting). The cavity emission spectrum is simulated for arbitrary T. It is shown that the spin-photon coherence can be partially preserved for T < w sqrt{N}/2, where w is the spin excitation energy, even in case when the spins are randomly directed. The calculations corroborate recent room-temperature observations of the collective coupling between the microwave cavity mode and the electron spin ensemble (NV centers in diamond, DPPH, Fe8 nanomagnets). At higher T, as a consequence of thermal excitations within the spin ensemble, the two lines of the emission spectrum merge into a narrow line with broad wings.

Investigations of information quantifiers for the Tavis–Cummings model

In this article, a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via a multi-photon transition is considered. The quantum Fisher information, negativity, classical Fisher information, and reduced von Neumann entropy for the two atoms are investigated. We found that the number of photon transitions plays an important role in the dynamics of different information quantifiers in the cases of two symmetric and two asymmetric atoms. Our results show that there is a close relationship between the different quantifiers. Also, the quantum and classical Fisher information can be useful for studying the properties of quantum states which are important in quantum optics and information.

Effects of Cavity-Field Statistics on Atomic Entanglement in Two-Mode Jaynes-Cummings Model

We study the entanglement properties of a pair of two-level Rydberg atoms passing one after another into a lossless cavity with two modes. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the cavity field results in the final two-atom mixed entangled type state. The entanglement of formation of the joint two-atom state as a function of the Rabi angle gt is calculated for Fock state field, coherent field and thermal field respectively inside the cavity. We present a comparative study of two-atom entanglement corresponding to the different field statistics.

A quantum description of radiation damping and the free induction signal in magnetic resonance

We apply the methods of cavity quantum electrodynamics (CQED), to obtain a microscopic and fully quantum-mechanical picture of radiation damping in magnetic resonance, and the nascent formation of the free induction signal. Numerical solution of the Tavis-Cummings model - i.e., multiple spins 1∕2 coupled to a lossless single-mode cavity - shows in fine detail the transfer of Zeeman energy, via spin coherence, to excite the cavity - represented here by a quantized LC resonator. The case of a single spin is also solved analytically. Although the motion of the Bloch vector is non-classical, we nonetheless show that the quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and stimulated emission) gives realistic estimates of macroscopic signal strength and the radiation damping constant in nuclear magnetic resonance. We also show how to introduce dissipation: cavity losses by means of a master equation, and relaxation by the phenomenological method of Bloch. The failure to obtain the full Bloch equations (unless semi-classical conditions are imposed on the cavity) is discussed in light of similar issues arising in CQED (and in earlier work in magnetic resonance as well), as are certain problems relative to quantization of the electromagnetic near-field.

Effects of cavity-field statistics on atomic entanglement in a two-mode Jaynes–Cummings model with intensity-dependent coupling

We study the entanglement properties of a pair of two-level Rydberg atoms passing one after another into a lossless cavity with two modes. The atoms interact with the cavity field via an intensity-dependent, non-degenerate two-photon transition. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the two-mode cavity photon field result in the final two-atom mixed entangled type state. The entanglement of formation of the joint two-atom state as a function of the Rabi angle, gt, is calculated for the two-mode Fock state field, coherent field, and thermal field, respectively, inside the cavity. The change in the magnitude of atomic entanglement with cavity photon number in two modes has been studied.

APPROXIMATE STABILIZATION OF AN INFINITE DIMENSIONAL QUANTUM STOCHASTIC SYSTEM

We study the state feedback stabilization of a quantum harmonic oscillator near a pre-specified Fock state (photon number state). Such a state feedback controller has been recently implemented on a quantized electromagnetic field in an almost lossless cavity. Such open quantum systems are governed by a controlled discrete-time Markov chain in the unit ball of an infinite dimensional Hilbert space. The control design is based on an unbounded Lyapunov function that is minimized at each time-step by feedback. This ensures (weak-*) convergence of probability measures to a final measure concentrated on the target Fock state with a pre-specified probability. This probability may be made arbitrarily close to 1 by choosing the feedback parameters and the Lyapunov function. They are chosen so that the stochastic flow that describes the Markov process may be shown to be tight (concentrated on a compact set with probability arbitrarily close to 1). Convergence proof uses Prohorov's theorem and specific properties of this Lyapunov function.

Cavity Resonator Measurement of Dielectric Materials Accounting for Wall Losses and a Filling Hole

A cavity resonator technique for the measurement of isotropic homogeneous nonmagnetic dielectric materials is addressed. The materials to be measured are placed in a well-defined position inside a circular cylindrical cavity resonator through a filling hole in the head end cap of the resonator. The measurement procedure solves the inverse problem based on a variational formulation in terms of the magnetic field in the resonator. The effects of lossy walls and of the filling hole are taken into account by using inhomogeneous surface impedance boundary conditions. In order to reduce the problem to matrix form, the magnetic field in the variational formulation is expanded in terms of undamped eigenmodes of the lossless cavity. The resulting equation is a generalized eigenvalue problem for the unknown material parameters. It is solved by using standard techniques such as the generalized Schur decomposition. The proposed method is tested against experimental data, including measurements at various temperatures, in order to show its capabilities as well as to see the effect of the filling hole on the results.

ENTANGLEMENT OF TWO DIPOLE-COUPLED ATOMS INTERACTING WITH TWO-MODE THERMAL FIELD IN THE CAVITY WITH HIGH TEMPERATURE

The entanglement of two dipole-coupled atoms with nondegenerate two-photon transitions interacting with two-mode field in lossless cavity has been investigated. The possibility of considerable growth of atomic entanglement is shown in the case of great mean values of thermal photons.

The effect of silicon loss and fabrication tolerance on spectral properties of porous silicon Fabry-Perot cavities in sensing applications

In this paper, we investigate the effect of non-uniformities (enlargement of current passage, non-equal surface current densities, etc.) in axial as well as transverse directions of a porous silicon Fabry-Perot (FP) cavity as well as loss nature of bulk silicon on spectral properties of this cavity, even that cavity is created with an anisotropic etching process. Without correct and comprehensive characterization of such cavities by incorporating these non-uniformities and inherent lossy nature of a cavity, detection and identification of biological and chemical molecules by that cavity may yield unpredictable and misleading results. From our simulations, we note the following two key points. First, effects of the refractive index and the thickness of microcavity region of a lossless or lossy FP cavity on resonance wavelength is more prevailing than those of first and last layers. Second, the effect of some small loss inside the FP cavity is not detectable by the measurement of resonance wavelength whereas the same influence is noticeable by the measurement of reflectivity. We carried out some measurements from two different regions on the fabricated cavities to validate our simulation results. From a practical point of view in correct detection and/or identification of lossy biological or chemical vapor by FP cavities, we conclude that not only the measurement of resonance wavelength as well as its shift but also the reflectivity value at the resonance wavelength or some specific wavelengths should be utilized.

Dynamics of the Two Atoms Interacting with Quantized Two Modes Cavity Fields in the Ladder Configuration

Exact solutions are obtained for the collective model of two identical two level atoms interacting with a quantized bimodal-field in a lossless cavity. A unitary transformation method is used to solve the time-dependent problem, that also gives the eigensolutions of the interacting Hamiltonian. In particular, we study the atomic population dynamics and the dynamics of the photon statistics in the two cavity modes. We present evidence of co-operative effects.

Dynamics for two atoms interacting with intensity-dependent two-mode quantized cavity fields in the ladder configuration

Exact solutions are obtained for a collective model of two identical two-level atoms interacting with a quantized bimodal field with intensity-dependent coupling terms in a lossless cavity. A unitary transformation method is used to solve the time-dependent problem that also gives the eigensolutions of the interaction Hamiltonian. The atomic population dynamics and the dynamics of the photon statistics of the two cavity modes are studied. We present evidence of cooperative effects.

Exact Solutions for Two-Channel Cavity QED Model by Unitary Transformation Method

A fully quantum mechanical picture for an atomic system interacting with two modes in a lossless cavity is presented. It is assumed that one of the modes interacts with the atom through three-photon process and the other one through a single-photon process. The effect of intensity dependent coupling between the atom and the two field modes has also been analyzed. The Unitary Transformation Method presented here not only solves the time dependent problem but also provides the eigensolutions of the interacting Hamiltonian at the same time.

Asymmetric focusing study from twin input power couplers using realistic rf cavity field maps

Advanced simulation codes now exist that can self-consistently solve Maxwell's equations for the combined system of an rf cavity and a beam bunch. While these simulations are important for a complete understanding of the beam dynamics in rf cavities, they require significant time and computing power. These techniques are therefore not readily included in real time simulations useful to the beam physicist during beam operations. Thus, there exists a need for a simplified algorithm which simulates realistic cavity fields significantly faster than self-consistent codes, while still incorporating enough of the necessary physics to ensure accurate beam dynamics computation. To this end, we establish a procedure for producing realistic field maps using lossless cavity eigenmode field solvers. This algorithm incorporates all relevant cavity design and operating parameters, including beam loading from a nonrelativistic beam. The algorithm is then used to investigate the asymmetric quadrupolelike focusing produced by the input couplers of the Cornell ERL injector cavity for a variety of beam and operating parameters.