Field In Coherent State Research Articles

Properties of field quantum entropy evolution in the Jaynes–Cummings model with initial squeezed coherent states field

The properties of the field quantum entropy evolution in a system of a single-mode squeezed coherent state field interacting with a two-level atom is studied by utilizing the complete quantum theory, and we focus our attention on the discussion of the influences of field squeezing parameter γ, atomic distribution angle θ and coupling strength g between the field and the atom on the properties of the evolution of field quantum entropy. The results obtained from numerical calculation indicate that the amplitude of oscillation of field quantum entropy evolution decreases with the increasing of squeezing parameter γ, and that both atomic distribution angle θ and coupling strength g between the field and the atom can influence the periodicity of field quantum entropy evolution.

Generation of a coherent superposition of a travelling wave field

We propose an experimentally feasible scheme to generate a superposition of travelling field coherent states using an extremely small Kerr effect and an ancilla which could be a single photon or two entangled twin photons. The scheme contains ingredients which are all within the current state of the art and is robust against the main sources of errors which can be identified in our setups.

Dipole squeezing in the system of the two-mode entangled coherent field interacting with atoms in Bell states in Kerr medium

The atomic dipole squeezing effect in the system of two identical two-level atoms in the Bell state interacting with the two-mode entangled coherent state field in Kerr medium are investigated by means of solving the Schrdinger equation and numerical calculations. The effects on the atomic dipole squeezing effect produced by the atomic initial state, mean photon number of light field, the degree of the entanglement of the entangled coherent field, the coupling strength of the Kerr medium with the light field and the coupling strength of dipole-dipole interaction between atoms are discussed. The results show that the dipole squeezing effect does not appear for the Bell state |β11>, while there can be dipole squeezing effect under certain conditions for the Bell states |β00> or |β01> or |β10>. In the latter case, the dipole squeezing effect depends on the coupling strength of the Kerr medium with the light field, the mean photon number and the degree of entanglement of the two-mode entangled coherent field.

Nonclassical properties in the resonant interaction of a three level wedge-type atom with two-mode field in coherent state

In this paper, we study the nonclassical properties of the electromagnetic field resulting from the interaction of a three-level ∧-type atom with a two-mode field initially in the coherent state, such as squeezing properties and sub-Poisson statistics. We show that the squeezing can be enhanced by selective atomic measurement.

Generation of quantum switch and nonlocal fields with an external field in a high quality dispersive cavity

We present a scheme to prepare an optical “quantum switch”, a superposition of “open” and “closed” states. The scheme is based on the interaction of an Λ-type three-level atom with a single-mode of quantized cavity field and an external classical driving field, in the regime where the atom and fields are highly detuned. We show how this interaction can be used to generate coherent states of the cavity field in contrast to the usual method used in microwave cavity QED of injecting a coherent state into a cavity. A combination of switches could be used to prepare a quantum superposition of coherent field states located simultaneously in two cavities. Compared with previous proposals, our scheme is simplified due to economizes the Ramsey zone and the time required for the state generation is short.

Conditional preparation of X (2) macroscopic entangled states

Two experimental arrangements consisting of coupled spontaneous parametric down-converters with type-I phase matching pumped simultaneously by a powerful optical field in a coherent state through a balanced beam splitter and linear optical elements are proposed for conditional preparation of macroscopic entangled states in output pumping modes of the studied system. Successful generation of the macroscopic entangled state in the pumping modes is unambiguously heralded by coincident detection of two photons in the generated signal and idler modes of the system. We calculate the amount of entanglement and probabilities of successfully observing the X (2) macroscopic entangled states in the total wavefunction. We show that the proposed schemes can be used to obtain a new type of macroscopic entangled states.

Entanglement of Non-symmetric Two Atomic Qubits Induced by aCoherent State Field

The entanglement of two atomic qubits, which arecoupled to a coherent state field with different couplings, is studied. Thedynamical evolution of the concurrence, which measures the degree of theentanglement between the two qubits, is plotted versus the scaledtime gt.It is found that the two qubits can be entangled by the coherent state fieldeven when they are initially prepared in the most mixed state, and for veryweak field, the most mixed state can be more easily entangled than some purestates. It is also found that the entanglement between the qubits sensitivelydepends on the relative difference of the atomic couplings and the meanphoton number of the field.

Emission and cavity-field spectra in a cascade three-level system interacting with a single-mode field

By using the method of eigenvalues and eigenstates, the emission and cavity-field spectra of a cascade three-level atom interacting with a single-mode electromagnetic field are studied in both intensity-dependent coupling (IDC) and intensity-independent coupling (IIC) cases. The photon statistics of the field on the spectra are investigated for the initial field in the pure number state, the coherent state and the thermal state. In the resonant case and the strong field limit, the pure-number-state emission spectrum exhibits six peaks and three peaks, respectively, for the IDC case and the IIC case. For a strong initial coherent state field or a strong thermal state field, the central structure of the emission spectrum at the field frequency is a doublet in the IDC case and a singlet in the IIC case. The cavity-field spectrum has three peaks in the IDC case and a single peak in the IIC case in the strong field limit for all of the three kinds of initial fields considered. Results indicate that in the emission spectrum merging of spectral peaks occurs for the IIC case as the initial field becomes stronger while it does not happen for the IDC case.

Generation of Entanglement Between Two Noninteracting Qubitsvia Interaction with Nonclassical Radiation Field**The project supported byNational Natural Science Foundation of China under Grant No. 10374007

We study the interaction between a single-mode quantized fieldand a quantum system composed of two qubits. We suppose that two qubitsinitially be prepared in the mixed and separable state, and studyhow entanglement between two qubits arises in the course ofevolution according to the Jaynes–Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem.When the qubits are initially prepared in the maximally mixed andseparable state, for coherent state field we cannot findentanglement between two qubits; for squeezed state fieldentanglement between two qubits exists in several short period of time; for evenand odd coherent state fields of large photon number, the dynamicalbehavior of the entanglement between two qubits shows collapseand revival phenomenon. For odd coherent state field of smallphoton number, the entanglement with both qubitsinitially prepared in maximally mixed state can be stronger than thatwith both qubits initially prepared in pure states. For fields ofsmall photon number, the entanglement stronglydepends on the states they are initially prepared in. For coherentstate field, and odd and even coherent state fields of large photonnumber, the entanglement only depends on the purity of the initialstate of qubit subsystem. We also show that during the evolutionthe unentangled state may be purer than the entangled state, andthe maximum degree of entanglement may not occur at the time whenthe qubit subsystem is in the purist state.

Classical limit of the interaction of a quantum system with the electromagnetic field

The interaction of nonrelativistic matter with the quantized electromagnetic field is investigated in the classical limit of large photon numbers. Quantization of both matter, say an atom, and the field results in a time-independent Schr\"odinger equation (TISE). However, for very strong fields (quantum mechanically, large photon numbers) this is impractical to solve. The standard approach then is simply to replace the quantized field by a classical field to give a time-dependent Schr\"odinger equation (TDSE) for the atom alone. Here we show how this TDSE can be derived from the TISE for atom plus field, illustrating at each stage the approximations that are necessary to treat the field classically. An important difficulty at the semiclassical stage is a breakdown of the approximation at classical turning points. We show how the use of coherent field states can circumvent this problem. In the limit that the field can be treated classically, time emerges from the Maxwell equations and a TDSE for the atom alone results.

Transfer-matrices of coherent state path integrals with the h4- and su(2)-algebra for many-body systems with contact interactions

Spatial transfer-matrices are constructed for 1D su(2)-spin and h 4-bosonic many-body systems in external magnetic fields B( x) or potentials V( x). In the case of the spin system, generalized coherent states are applied to derive a path integral which can be reordered according to the spatial position of the generalized coherent state fields. The spatial generator of the transfer-matrix for the spin system consists of a so(3) Laplace operator and a term with the external magnetic field B( x). It is also demonstrated that generalized differential transfer-matrix equations can be obtained for disordered many-body systems if the ensemble-averaged coherent state path integral of the random potentials contains only contact interactions and nearest-neighbour couplings from the kinetic energy.

Functional integral and transfer-matrix approach for 1D bosonic many-body systems with a contact potential

A 1D bosonic many-body system, related to the Bose–Einstein condensation in atomic traps and periodic optical lattices, is described by a coherent state path integral of the grand canonical partition function. Since the interaction is given by a contact potential, as commonly applied in atomic traps of BEC, the functional integral can be represented by spatial transfer matrices, ordered according to their sequential position in space. The corresponding differential transfer matrix equation is derived and the generator H(φ,x) for space translations is given, including an approximation of slowly varying coherent state fields. The given approach of spatial transfer matrices contains large fluctuations and higher order correlation functions beyond the mean field approximation and, in analogy, can be compared to the time development operator of the Feynman path integral and the one-particle Schrödinger equation. It is also described how to obtain the spatial transfer-matrix or its corresponding generator for 2D bosonic systems and also fermions with a quartic contact interaction which leads to a differential equation with Grassmann numbers.

Higher-order squeezing for atomic dipole of a three-level atom in the kerr-like medium cavity fields

In this paper, evolution of the higher-order squeezing for atomic dipole of three-level atom in the Kerr-like medium is investigated. The atom discussed has two configurations and is driven by the single-mode coherent state field. Our results show that the squeezing effects are clearly influenced by nonlinear parameters, the initial atom state and the detuning.

One-sided atomic deflection in the optical Stern-Gerlach effect and coherent trapping

In the optical Stern-Gerlach effect, the interaction of a traveling two-level atom with the electromagnetic field of an optical cavity causes a splitting of the atomic trajectory. One may ask if it is possible to single out particular initial configurations of the system that will lead to selective scattering, in which the atoms follow only one trajectory. We show that these configurations consist of a coherent superposition of the atomic internal states, and of a field phase state or a field coherent state, with a precise phase relation between the two subsystems: The same configurations which produce the so-called atomic coherent trapping in the Jaynes-Cummings model.

Emission spectrum of a Λ-type three-level atom driven by a two-mode field

An analytical expression of emission spectrum for Λ-type three-level atom interacted with two-mode cavity field is given. The characters of the emission spectrum for the field in photon number state, coherent state and SU(2) coherent state are exhibited. The effects of the atomic initial state, the field property on the time-dependent physical spectrum are analyzed.

A joint Wigner function of an atom-field system with dissipation

We found analytically the exact joint Wigner function (WF) of an atom-field system described by the Jaynes-Cummings model in the dispersive limit for a given initial state. Using the solution of a master equation with a dissipative term calculated by Peixoto de Faria and Nemes (Peixoto de Faria J G and Nemes M C 1999 Phys. Rev. A 59 3918) and a general expression for the joint WF proposed by Czirjak and Benedict (Czirjak A and Benedict M G 1996 Quantum Semiclass. Opt. 8 975), we obtained the exact reduced atom and field WFs and analysed their time evolution. Our results show that, at the maximum entanglement times, the atom tends to a statistical mixture state represented by a spherical polar plot. Also, the atomic WF shows how fast the negative-valued part disappears as a function of dissipation constant and the strength of the field coherent state.

Atom lasers, coherent states, and coherence II. Maximally robust ensembles of pure states

As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of $\rho_{ss}$, is more natural. In the preceding paper we concentrated upon whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy $\chi$ of the bosons in the laser mode, and the excess phase noise $\nu$. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit ($\nu=\chi=0$), the most robust states are coherent states. As the phase noise $\nu$ or phase dispersion $\chi$ is increased, the most robust states become increasingly amplitude-squeezed. We find scaling laws for these states. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR states having a well-defined coherent amplitude. This lends support to the idea that robust PR ensembles are the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.

Preparation and decoherence of superpositions of electromagnetic field states

In a recent experiment the progressive decoherence of a mesoscopic superposition of two coherent field states in a high-Q cavity, known as Schrodinger cat state, has been measured for the first time [Brune et al., Phys. Rev. Lett. 77, 4887 (1996)]. Here, the full master equation governing the coupled dissipative dynamics of the atom-field system studied in the experiment is formulated and solved numerically for the experimental parameters. The model simulated avoids the approximations underlying an analytically solvable model which is based on a harmonic expansion of the energies of the dressed atomic states and on a treatment of their dynamics within the adiabatic approximation. In particular, the numerical simulations reveal that the coupling of the cavity field mode to its environment causes important decoherence effects already during the initial preparation phase of the Schrodinger cat state. This phenomenon is investigated in detail with the help of a measure for the purity of states. Moreover, the Hilbert-Schmidt distance of the intended target state, the Schrodinger cat, to the state that is actually prepared in the experiment is determined.

Thermal Squeezed State Representation of Scalar Field and Energy Density in Semiclassical Theory of Gravity

The semiclassical theory of gravity is studied in terms of representation of scalar field in thermal coherent state and thermal squeezed state formalisms. For the FRW cosmological model with a minimal scalar field, the semiclassical Einstein equation reduces to zero-point energy term plus a finite temperature term and classical term in thermal coherent state. In thermal squeezed vacuum state it reduces to quantum term in addition to the finite temperature term and zero-point energy term. The present study can account for nonclassical state and finite temperature effect contributions to energy density in semiclassical theory of gravity.

Simplified realization of multi-atom Greenberger–Horne–Zeilinger states with dispersive cavity QED

We propose a simple scheme for the generation of multi-atom Greenberger–Horne–Zeilinger (GHZ) states. Three appropriately prepared atoms are sent through a nonresonant cavity filled with a coherent field. The whole system evolves into an entangled state, in which two three-atom maximally entangled states are correlated with coherent field states separated by π in phase space. The field is then driven by a classical current and measured by an atom, which collapses the atomic system onto a GHZ state. The scheme can be easily generalized to prepare n-atom maximally entangled states.