Creating quantum entanglement between multi-atom Dicke states and two cavity modes

We present a scheme to create quantum entanglement between multi-atom Dicke states and two cavity modes by passing N three-level atoms in Λ configuration through a resonant two-mode cavity one by one. We further show that such a scheme can be used to generate arbitrary two-mode N-photon entangled states, arbitrary superposition of Dicke states, and a maximal entangled state of Dicke states. These states may find applications in the demonstration of quantum non-locality, high-precision spectroscopy and quantum information processing.     

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.     

Preparation of W,GHZ, and two-qutrit states using bimodal cavities

Abstract

We show how one can prepare three-qubit entangled states like W-states, Greenberger-Horne-Zeilinger states as well as two-qutrit entangled states using the multi-atom two-mode entanglement. We propose a technique of preparing such a multi-particle entanglement using stimulated Raman adiabatic passage. We consider a collection of three-level atoms in Λ configuration simultaneously interacting with a resonant two-mode cavity for this purpose. Our approach permits a variety of multi-particle extensions.     

Tripartite entanglement generation using cavity-QED and its dynamics in dissipative environments

We investigate the generation of tripartite field states inside the high-Q cavities using the cavity QED. The main goal is to successfully generate the entanglement in tripartite systems by passing two-level atoms through three identical high-Q cavities. Our scheme gives the successful generation of entangled tripartite W and GHZ states for pre-determined interaction times of atoms with the cavity fields. The dynamics of initial entangled states is studied as the system evolves in the dissipative environments.     

Effect of the Stark shift on entanglement in a double two-photon JC model

Considering a double two-photon JC model, we investigate the entanglement between the two two-level atoms and that between the two cavity fields, and study the effect of the Stark shift on entanglement. The results show that, on the one hand the atom–atom and cavity–cavity concurrences evolve periodically with time and the periods are affected by the Stark shift; on the other hand, the two atoms are not disentangled at any time when the Stark shift is considered, and for large values of the Stark shift parameter, the two atoms can remain in a stationary entangled state. In addition, we find that the so-called entanglement sudden death can occur under appropriate conditions on the dynamic Stark shift for a certain initial state of the system.     

Controlling entanglement dynamics of two qubits coupled to a common reservoir via a coherent field

We investigate the time evolution of entanglement between two two-level atoms which are coupled to a common multimode electromagnetic reservoir and simultaneously driven by a coherent field. We find that the entanglement can always be created and maintained with a moderate intensity of the driving field during the track of approaching steady entangled states when both atoms are initially in their ground states and the reservoir is in the vacuum state or the squeezed vacuum state. We also show that the steady-state entanglement between the atoms can be enhanced by use of the coherent field when the reservoir is in the weakly squeezed vacuum state. More interestingly, in the squeezed reservoir case, the sudden death period in the time evolution of the entanglement can be removed by use of the coherent driving field.     

Time evolution of entanglement and bistability of two coupled quantum dots in a driven cavity

Abstract

The time evolution of entanglement between two quantum dots (QDs) trapped inside a cavity driven by a coherent quantized field is studied. In the presence of dissipation, entanglement shows many interesting features such as sudden death and revival, and finite steady state value after sudden death. We also investigate dependence of entanglement on dot variables and its relation to bistability. It is found that entanglement vanishes when the cavity field intensity approaches the upper branch of the bistability curve. When the cavity is driven by a modulated field in the presence of dissipation, it can periodically generate entanglement, which is much larger than the maximum value attained in the steady-state for this system but the dots are never fully entangled.     

Entangled Coherent States with Variable Weighting

Abstract

Entangled coherent states, with arbitrary weighting of the two product coherent states in the superposition, might be produced by incorporating an optical bistable device in a coupled cavity configuration. This scheme is contrasted with the entangled coherent states that arise due to interaction in an optical Kerr medium and produce only equally weighted entanglements. The entanglement is shown to occur, not between coherent states, but between states which closely approximate coherent states. An interaction which does produce entanglement between true coherent states is introduced but is shown to be unphysical.     

Typical entanglement in multiple-qubit systems

Quantum entanglement and its paradoxical properties hold the key to an information processing revolution. Much attention has focused recently on the challenging problem of characterizing entanglement. Entanglement for a two qubit system is reasonably well understood; however, the nature and properties of multiple qubit systems are largely unexplored. Motivated by the importance of such systems in quantum computing, we show that typical pure states of N qubits are highly entangled but have decreasing amounts of pairwise entanglement (measured using the Wootter concurrence formula) as N increases. Above six qubits, very few states have any pairwise entanglement and, generally, for a typical pure state of N qubits there is a sharp cut-off where its subsystems of size m become positive partial transpose (i.e. separable or only bound entangled) around N ? 2m + 3, based on numerical analysis up to N = 13.     

Continuous variable entanglement purification and its physical implementation

Abstract

We describe in detail an entanglement purification protocol which generates maximally entangled states with high efficiencies from realistic Gaussian continuous variable entangled states. A physical implementation of this protocol which uses high finesse cavities and cavity enhanced cross-Kerr nonlinearities is analysed.     

Meeting Report

Abstract

The cooperative dynamics of a microlaser consisting of two threelevel atoms interacting with a pump field and two quantized cavity modes forming a radiative cascade are studied. Adiabatic elimination of one mode leads to a strong dynamical entanglement between the internal states of the atoms which allows us to study the effects of a cavity-mediated dipole-dipole interaction. We show that the coherent dynamics of the two-atom system will preferentially couple symmetrical linear combinations of internal states. If this coupling dominates the dynamics, the two-atom system will behave like a single atom with correspondingly larger dipole moment, that is a superradiant two-atom system. Even very small spontaneous decay causes transitions from symmetrical to antisymmetrical states and conversely. The hopping between two subsets of the state space can give rise to intriguing phenomena such as bistability of the laser mode intensity. By a randomization of the two coupling phases we recover the standard independent-atom laser theory.     

Cooperativity and Entanglement of Atom-field States

Abstract

The Jaynes-Cummings model of a single two-level atom interacting with a quantized single-mode coherent field generates at the half-revival time a dynamically disentangled atom-field state. At such times, the field is in asymptotically pure Schrödinger cat state, a macroscopic superposition of distinct field eigenmodes. In this paper we address the problem of field purity when a second atom is allowed to interact with the cavity mode and becomes entangled with the first atom via their mutual cavity field with which they interact. We employ the collective Dicke states to describe the cooperative effects on the entanglement and show that the second atom spoils the purity of the field state except for special cases of the atom-field coupling or of initial conditions.     

Entanglement distillation from Gaussian input states by coherent photon addition

The entanglement between Gaussian entangled states can be increased by non-Gaussian operations. We design a new scheme, named coherent photon addition, which can coherently add one photon generated by a spontaneous parametric down-conversation process to Gaussian quadrature-entangled light pulses created by a non-degenerate optical parametric amplifier. This operation can increase the entanglement of input two-mode Gaussian states as an entanglement distillation, and provides us with a new method of non-Gaussian operation. This scheme can also help us to study the decoherence of adding one- to two-mode Gaussian states from coherent photon addition to normal photon addition.     

Encoding and decoding in complementary bases with quantum gates

Abstract

The total information content of a composite system consisting of k qubits can either be completely encoded in a specific computational basis, or alternatively it can be partially encoded in a number of different bases. In that case the information encoded in a complete set of mutually complementary bases is again k bits. Using only two single-qubit gates and the controlled-NOT gate, one can implement coding and decoding in such a complete set. The total information content is then invariant under the particular choice of a complete set of mutually complementary bases. For maximally entangled states the k bits of information are not encoded into the k qubits separately but only into their joint properties.     

Entanglement between two atoms interacting with a stochastic field

The entanglement property between two two-level atoms interacting with a stochastic field is studied. We analytically prove that when the correlation time κ ^?1 of the stochastic field is very short compared to the radiative lifetime γ ^?1 of the atom, the steady-state entanglement between the two atoms can appear. The concurrence characterizing the entanglement degree has also been calculated by using Monte Carlo simulation. It is shown that the correlation time has a strong effect on the entanglement. We also discuss the influence of strength of the stochastic process on the entanglement. The validity of the decorrelation approximation is also investigated.     

Cavity QED analog of spin

Abstract

Using the even and odd coherent states, we show that a single mode cavity field, prepared in a coherent state by a classical source and manipulated by both dispersive and resonant interactions with atoms, is analogous to a spin one-half particle interacting with Stern–Gerlach magnets where the parity of the field is the analog of spin. Because the number of photons in the cavity may be large, the system we describe can exhibit quantum effects on at least a mesoscopic scale. We show that entangled two and three cavity systems can be generated. The three cavity case can be used to demonstrate the contradiction between local realistic theories and quantum mechanics in the manner proposed by Greenberger, Horne and Zeilinger in 1989 [13].     

Experimental detection of entanglement via witness operators and local measurements

Abstract

In this paper we address the problem of detection of entanglement using only few local measurements when some knowledge about the state is given. The idea is based on an optimized decomposition of witness operators into local operators. We discuss two possible ways of optimizing this local decomposition. We present several analytical results and estimates for optimized detection strategies for NPT states of 2 × 2 and N × M systems, entangled states in 3 qubit systems, and bound entangled states in 3 × 3 and 2 × 4 systems.     

Enhanced entanglement in a non-degenerate four-level atom with a parametric oscillator

We discuss the generation and evolution of a macroscopic entanglement light with a subthreshold non-degenerate parametric oscillator, coupled to a vacuum reservoir. The four-level atoms driven by two classical fields interact with the parametric oscillator. The master equation for the cavity modes of the scheme is derived and analyzed, the entanglement properties of the two-mode light generated by this scheme inside and outside the cavity is studied. We show that the light produced by this system is strongly entangled with time evolution inside and outside a cavity.     

Entanglement-induced population trapping by Schrödinger's cat

Abstract

We propose an experiment that is a variation of the Schrödinger's cat ′paradox' wherein the entanglement between a microscopic system and a macroscopic system is of primary interest. The experiment involves tunable entanglement and serves as a model for controllable decoherence in the context of cavity quantum electrodynamics where atoms interact dispersively with a cavity field initially in a coherent state. The interaction produces an entanglement between the atom and the field, and the degree of entanglement can be probed by subjecting the atom to resonant classical radiation after it leaves the cavity. The amplitude of the resulting Rabi oscillations reflects the degree of the entanglement, there being no Rabi oscillations when the entanglement is maximum. We show that the cavity damping does not affect the experiment.     

Entanglement induced by spontaneous emission in spatially extended two-atom systems

Abstract

The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.