Field Entanglement Research Articles

Dynamics of an atom coupled through a parametric frequency converter with quantum and classical fields

In this communication we introduce a model of a two-level system which represents the interaction between an atom and external quantum and classical electric fields through a parametric frequency converter. We show that the system can be reduced to an effective Jaynes–Cummings model by adequate adjustment of the field coupling in the frequency converter. The atom dynamics and the atom-quantum field entanglement are then shown to be controlled through the classical field.

QUANTUM ENTANGLEMENT IN THE SYSTEM OF ATOMS IN BELL STATE INTERACTING WITH THE TWO-MODE ODD–EVEN ENTANGLED COHERENT FIELD

We studied the entanglement properties of the system consisting of two atoms in Bell states interacting with the two-mode odd-even entangled coherent field by utilizing the complete quantum theory. The influences of the initial Bell state of the atoms, the intensity of field, the coupling strength of interaction between atoms and the initial degree of the entanglement between the two-mode fields on the atomic entropy and on negativity are discussed by using numerical calculations. It turns out that the two atoms can keep their initial maximal entangled state while the two-atom and the two-mode field keep their initial disentangled state if the two atoms are initially in |β11〉. Therefore, for the initial atomic state |β00〉 or |β01〉, the increasing of the field intensity can be a help to prepare the atom-field entanglement, and for |β10〉, it is beneficial for the atom–atom entanglement. Meanwhile, for the initial atomic state |β10〉 and |β01〉, strong coupling strength of interaction between atoms is beneficial for the atom–atom entanglement, but for |β00〉, it can be helpful for the atom-field entanglement.

Entanglement of fields in coupled cavities: Effects of pumping and fluctuations

A system of two coupled cavities is studied in the context of bipartite, continuous variable entanglement. One of the cavities is pumped by an external classical source that is coupled quadratically, to the cavity field. Dynamics of entanglement, quantified by covariance measure [V.V. Dodonov, et al., Phys. Lett. A 296 (2002) 73], in the presence of cavity–cavity coupling and external pumping is investigated. The importance of tailoring the coupling between the cavities is brought out by studying the effects of pump fluctuations on the entanglement.

Spatial two-photon coherence of the entangled field produced by down-conversion using a partially spatially coherent pump beam

We study the spatial coherence properties of the entangled two-photon field produced by parametric down-conversion (PDC) when the pump field is, spatially, a partially coherent beam. By explicitly treating the case of a pump beam of the Gaussian Schell-model type, we show that in PDC the spatial coherence properties of the pump field get entirely transferred to the spatial coherence properties of the down-converted two-photon field. As one important consequence of this study, we find that, for two-qubit states based on the position correlations of the two-photon field, the maximum achievable entanglement, as quantified by concurrence, is bounded by the degree of spatial coherence of the pump field. These results could be important by providing a means of controlling the entanglement of down-converted photons by tailoring the degree of coherence of the pump field.

Entropy growth and degradation of entanglement due to phase decoherence in ion traps

We study how phase decoherence through intrinsic decoherence leads to growing entropy and a strong degradation of the maximum generated entanglement as a measure of information content of ionic state due to ion-laser interaction with a trapped ion. We calculate the partial entropy of the particle (atom or trapped ion) and field subsystems as well as the total entropy. The total entropy is shown to increase with time. Thus, the partial field or atomic entropy cannot be used as a direct measure of the particle–field entanglement. We find that, at least qualitatively, the difference between the total entropy and the sum of field and atom partial entropies can be used as an entanglement measure, when compared with an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix. We find a very strong sensitivity of the maximum generated entanglement on the decoherence and the chosen intrinsic decoherence parameter.

Entanglement of a coarse grained quantum field in the expanding universe

We investigate the entanglement of a quantum field in the expanding universe. By introducing a bipartite system using a coarse-grained scalar field, we apply the separability criterion based on the partial transpose operation and numerically calculate the bipartite entanglement between separate spatial regions. We find that the initial entangled state becomes separable or disentangled after the spatial separation of two points exceed the Hubble horizon. This provides the necessary conditions for the appearance of classicality of the quantum fluctuation. We also investigate the condition of classicality that the quantum field can be treated as the classical stochastic variables.

Quantum Entropy of a Nonlinear Two-level Atom with Atomic Motion

The wave function of a system governed by the time-dependent nonlinear Jaynes-Cummings (JC) model is obtained. We compute analytically the eigenvalues of the reduced field density operator by which the dynamics of the entropy of entanglement of the cavity field are analyzed. The influences of the atomic motion, the field-mode structure and the Kerr-like medium on this phenomenon are illustrated. The population dynamics of an excited atom is also discussed for the same set of parameters. The cavity field is assumed to be initially excited in either a Fock or a coherent states. The cavity excitation in a Fock state generates a class of an entanglement without death with fixed amplitude by adjusting the parameters of the atomic motion as well as the Kerr and the field-mode structure. In case of a coherent cavity, the only phenomenon to be noted is the periodical behavior of the dynamics under study when the atomic motion is considered. Although the Kerr medium affects the strength of the entanglement negatively, the entropy of entanglement loses its zeros where the Kerr is taken into consideration.

POLARIMETRIC DIAGNOSTICS OF UNRESOLVED CHROMOSPHERIC MAGNETIC FIELDS

For about a decade, spectro-polarimetry of HeI 10830 has been applied to the magnetic diagnostics of the solar chromosphere. This resonance line is very versatile, as it is visible both on disk and in off-limb structures, and it has a good sensitivity to both the weak-field Hanle effect and the strong-field Zeeman effect. Recent observations of an active-region filament showed that the linear polarization was dominated by the transverse Zeeman effect, with very little or no hint of scattering polarization. This is surprising, since the HeI levels should be significantly polarized in a conventional scattering scenario. To explain the observed level of atomic depolarization by collisional or radiative processes, one must invoke plasma densities larger by several orders of magnitude than currently known values for prominences. We show that such depolarization can be explained quite naturally by the presence of an unresolved, highly entangled magnetic field, which averages to give the ordered field inferred from spectro-polarimetric data, over the typical temporal and spatial scales of the observations. We present a modeling of the polarized HeI 10830 in this scenario, and discuss its implications for the magnetic diagnostics of prominences and spicules, and for the general study of unresolved magnetic field distributions in the solar atmosphere.

Spin and occupation number entanglement of Dirac fields for noninertial observers

We investigate the Unruh effect on entanglement taking into account the spin degree of freedom of the Dirac field. We analyze spin Bell states in this setting, obtaining their entanglement dependance on the acceleration of one of the partners. Then, we consider simple analogs to the occupation number entangled state |00>+|11>, but with spin quantum numbers for |11> showing that, despite their apparent similitude, while the spinless case is always qubit x qubit, for the spin case acceleration produces a qubit x qu4it state. We also introduce a procedure to consistently erase the spin information from our setting preserving occupation numbers. We show how the maximally entangled state for occupation number emerges from our setting, we also analyze its entanglement dependance on acceleration, obtaining a greater entanglement degradation than in the spinless case.

Quantum entanglement between the two-mode fields and atomic entropy squeezing in the system of a moving atom interacting with two-mode entangled coherent field

This paper investigates the entropy squeezing of a moving two-level atom interacting with the two-mode entangled coherent field via two-photon transition by using an entropic uncertainty relation and the degree of entanglement between the two-mode fields by using quantum relative entropy. The results obtained from numerical calculation indicate that the squeezed period, the duration of entropy squeezing and the maximal squeezing can be controlled by appropriately choosing the intensity of the light field, the atomic motion and the field-mode structure. The atomic motion leads to the periodic recovery of the initial maximal degree of entanglement between the two-mode fields. Moreover, there exists a corresponding relation between the time evolution properties of the atomic entropy squeezing and those of the entanglement between the two-mode fields.

Single-Photon Entanglement in the keV Regime via Coherent Control of Nuclear Forward Scattering

Generation of single-photon entanglement is discussed in nuclear forward scattering. Using successive switchings of the direction of the nuclear hyperfine magnetic field, the coherent scattering of photons on nuclei is controlled such that two signal pulses are generated out of one initial pump pulse. The two time-resolved correlated signal pulses have different polarizations and energy in the keV regime. Spatial separation of the entangled field modes and extraction of the signal from the background can be achieved with the help of state-of-the-art x-ray polarizers and piezoelectric fast steering mirrors.

ENTANGLEMENT OF A GENERAL FORMALISM Λ-TYPE THREE-LEVEL ATOM INTERACTING WITH A SINGLE-MODE FIELD IN THE PRESENCE OF NONLINEARITIES

We investigate the evolution of the atomic quantum entropy and the atom–field entanglement in a system of a Λ-configuration three-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system, we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium, and the intensity-dependent coupling functional on the entropy are analyzed.

Interference-induced enhancement of field entanglement from an intracavity three-levelV-type atom

We investigate the generation of two-mode-entangled light from a laser-driven three-level $\mathbsf{V}$-type atom inside a cavity by taking into account spontaneously generated quantum interference between two atomic decay channels. We show that under some conditions, the system can reduce to a nondegenerate parametric amplifier which is responsible for the entanglement between the two cavity modes. Compared to the case without the quantum interference, it is found that the entanglement of the cavity field can be significantly enhanced by the interference when the relative phase of the two pumping lasers $\ensuremath{\delta}\ensuremath{\phi}=\ensuremath{\pi}$.

Stationary state entanglement of a one-atom two-field system under random phase telegraph noise

In this paper, a system consisting of one atom coupled to two identical optical cavities in a stochastic interaction is investigated for the entanglement properties between the constituents by the Jaynes–Cummings model. The noise is considered to be the random phase telegraph noise and an exact solution of the model under this noise is obtained. The effects of the noise on the entanglement of the system reveal that the genuine three-partite entanglement cannot appear in the evolution of the system even in the presence of the random phase telegraph noise. The fields and the atom do not entangle with each other. However, the noise is cooperative and constructive in building a strong steady state field–field entanglement. Therefore, the separable state of the atom plays the role of a catalyst in the entanglement between the states of the cavity fields.

Conditions to preserve quantum entanglement of quadrature fluctuation fields in electromagnetically induced transparency media

We study the propagation of quantum fields through an electromagnetically induced transparency (EIT) medium with initially two squeezed and one coherent states. Conditions to preserve and to establish nonseparation criteria for perturbed quantized fluctuation fields are demonstrated. The results in this work provide a guideline for using EIT media as quantum light devices.

Entanglement transfer from superposed two-mode coherent states to two initially separable qubits

Entanglement transfer from the superposition states of the pair coherent states or the SU(1,1) coherent states to two initially separable qubits is investigated. The entropy of the superposition states has a novel property: there exists a maximum value when the phase difference between the two 2-mode coherent states is π. In the process of entanglement transfer from these superposition states to qubits, it is found that the qubits have the largest possible entanglement at the maximum of the entropy of the initial field, which shows a relationship between the entanglement of the initial field and that of the qubits. The concurrence of the qubits can periodically approach unity when the parameters of the initial field are properly chosen and the two qubits are initially at the ground states.

Output entanglement and squeezing of two-mode fields generated by a single atom

A single four-level atom interacting with two-mode cavities is investigated. Under large detuning condition, we obtain the effective Hamiltonian which is unitary squeezing operator of two-mode fields. Employing the input–output theory, we find that the entanglement and squeezing of the output fields can be achieved. By analyzing the squeezing spectrum, we show that asymmetric detuning and asymmetric atomic initial state split the squeezing spectrum from one valley into two minimum values, and appropriate leakage of the cavity is needed for obtaining output entangled fields.

Signal-to-noise ratio of Gaussian-state ghost imaging

The signal-to-noise ratios (SNRs) of three Gaussian-state ghost-imaging configurations---distinguished by the nature of their light sources---are derived. Two use classical-state light, specifically a joint signal-reference field state that has either the maximum phase-insensitive or the maximum phase-sensitive cross correlation consistent with having a proper $P$ representation. The third uses nonclassical light, in particular an entangled signal-reference field state with the maximum phase-sensitive cross correlation permitted by quantum mechanics. Analytic SNR expressions are developed for the near-field and far-field regimes, within which simple asymptotic approximations are presented for low-brightness and high-brightness sources. A high-brightness thermal-state (classical phase-insensitive state) source will typically achieve a higher SNR than a biphoton-state (low-brightness, low-flux limit of the entangled-state) source, when all other system parameters are equal for the two systems. With high efficiency photon-number-resolving detectors, a low-brightness, high-flux entangled-state source may achieve a higher SNR than that obtained with a high-brightness thermal-state source.

Solvable dynamics of N driven two-level atoms coupled to a dissipative cavity mode

We solve exactly the dynamics of N strongly driven two-level atoms equally coupled on resonance to a dissipative cavity mode. Analytical results are derived on decoherence, entanglement, purity, atomic correlations and cavity field mean photon number. Decoherence-free subspaces are predicted for the whole system and the N-qubit subsystem. Multi-partite entangled states and cavity cat-like states can be conditionally generated. The decay of quantum coherence and purity can be monitored by joint measurements on atomic populations. Atoms prepared in states invariant under permutation of any two components evolve within the subspace spanned by the completely symmetric Dicke states. Applications to N = 3, 4 are discussed.

Entropy correlation and entanglement for mixed states in an algebraic model

As an alternative with potential connections to actual experiments, other than the systems more usually used in the field of entanglement, the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well-established algebraic model, with parameters extracted from fitting to highly excited spectral experimental results for molecules H2O and SO2, is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode. For a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti-correlation. And the linear entropy of each mode is positively correlated with the negativities just for the mixed-squeezed states with small parameters in H2O while they do not display any correlation in other cases. For the mixed-squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy. The differences in the linear entropy and the negativities between H2O and SO2 are discussed as well. Those are useful for molecular quantum computing and quantum information processing.