We analyze the Einstein–Podolsky–Rosen (EPR) steering properties in a three-well Bose–Hubbard model under the mechanism of coherent transport of atomic population (CTAP). This process, also known as transport without transit (TWT), transfers condensed atoms from one well of a lattice potential to another, nonadjacent well, without macroscopic occupation of the middle well. The dynamics and entanglement properties of this system have previously been analyzed and shown to be dependent on the initial quantum state of the atoms in the first well. In this work we utilize the phase-space method of stochastic integration in the positive-P representation. The system demonstrated inseparability between the wells for Fock initial states, and we show that steering is also found only for an initial Fock state. Depending on how we write our steering inequalities, steering is seen at different times, showing a basic asymmetry. This means that for part of the evolution, Alice can steer Bob but not vice versa. After the midpoint of the population transfer, this situation reverses.
We analyze the Einstein–Podolsky–Rosen (EPR) steering properties in a three-well Bose–Hubbard model under the mechanism of coherent transport of atomic population (CTAP). This process, also known as transport without transit (TWT), transfers condensed atoms from one well of a lattice potential to another, nonadjacent well, without macroscopic occupation of the middle well. The dynamics and entanglement properties of this system have previously been analyzed and shown to be dependent on the initial quantum state of the atoms in the first well. In this work we utilize the phase-space method of stochastic integration in the positive-P representation. The system demonstrated inseparability between the wells for Fock initial states, and we show that steering is also found only for an initial Fock state. Depending on how we write our steering inequalities, steering is seen at different times, showing a basic asymmetry. This means that for part of the evolution, Alice can steer Bob but not vice versa. After the midpoint of the population transfer, this situation reverses.
Abstract We investigate the Einstein–Podolsky–Rosen (EPR) steering of two cavity modes generated via four-wave mixing processes. For a three-level V-type configuration, a strong coherent field as a dressing field couples the atoms, and a weak coherent field as a control filed resonantly couples one dressed state to the auxiliary state. By using the approach of dressed states and Bogoliubov modes, we find that only one Bogoliubov mode is mediated into the interaction with the dressed atoms, and the other one is decoupled. Due to the presence of the coherent control filed, the channel for dressed state population transfer is established, which plays a key role in the generation of the asymmetric EPR steering of two cavity fields. It is shown that the one-way EPR steering can be manipulated by the Rabi frequencies of the control field and the cooperativity parameters.
Quantum correlation is an important resource in quantum information, quantum computation, and quantum metrology. Quantum entanglement, Einstein-Podolsky-Rosen (EPR) quantum steering and Bell nonlocality are the major quantum correlations. For quantum entanglement and Bell nonlocality, two subsystems play the same significant roles. EPR quantum steering is stronger than entanglement and weaker than Bell nonlocality. It represents the ability of one subsystem to nonlocally affect another subsystem's states through local measurements. In this paper, the dynamic quantum correlation between the modes in the two-site Bose-Hubbard model is investigated. According to Hillery-Zubairy entanglement criterion and based on maximum mean quantum Fisher information, the influences of initial states on the quantum entanglement evolutions are explored. If the coupling between the modes is much greater than that of the particles at the same site, and the initial states are symmetric or anti-symmetric SU(2) coherent states, the quantum correlations show simple periodic evolutions. The oscillation amplitudes of the evolutions increase with the interaction between the particles at the same site. The oscillation period decreases with the coupling strength between the modes. The dependence of the period on the interaction of the particles at the same site is related to the initial states. In other words, the time evolutions of quantum correlation are closely related to the symmetry of the initial states. In the case of symmetric (anti-symmetric) SU(2) coherent state and repulsive (attractive) interaction of the particles at the same site, the system presents two-way quantum steering. When the subsystem exchange symmetry of the initial states is broken, the collapse and revival of quantum correlation appear, moreover one-way quantum steering emerges in the infancy. One-way quantum steering is asymmetric for two subsystems. So exchange asymmetry of the initial state is necessary condition of one-way quantum steering when the Hamiltonian of the system is symmetric for two subsystems.
Einstein–Podolsky–Rosen (EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world. The directivity (or asymmetry) is a fascinating trait of EPR steering, and it is different from other quantum nonlocalities. Here, we consider the strategy in which two atoms compose a two-qubit X state, and the two atoms are owned by Alice and Bob, respectively. The atom of Alice suffers from a reservoir, and the atom of Bob couples with a bit flip channel. The influences of auxiliary qubits on EPR steering and its directions are revealed by means of the entropy uncertainty relation. The results indicate that EPR steering declines with growing time t when adding fewer auxiliary qubits. The EPR steering behaves as damped oscillation when introducing more auxiliary qubits in the strong coupling regime. In the weak coupling regime, the EPR steering monotonously decreases as t increases when coupling auxiliary qubits. The increases in auxiliary qubits are responsible for the fact that the steerability from Alice to Bob (or from Bob to Alice) can be more effectively revealed. Notably, the introductions of more auxiliary qubits can change the situation that steerability from Alice to Bob is certain to a situation in which steerability from Bob to Alice is certain.
We consider two systems A and B that share Einstein–Podolsky–Rosen (EPR) steering correlations and study how these correlations will decay when each of the systems is independently coupled to a reservoir. EPR steering is a directional form of entanglement, and the measure of steering can change depending on whether system A is steered by B, or vice versa. First, we examine the decay of the steering correlations of the two-mode squeezed state. We find that if system B is coupled to a reservoir, then the decoherence of the steering of A by B is particularly marked, to the extent that there is a sudden death of steering after a finite time. We find a different directional effect if the reservoirs are thermally excited. Second, we study the decoherence of the steering of a Schrödinger cat state, modeled as the entangled state of a spin and harmonic oscillator, when the macroscopic system (the cat) is coupled to a reservoir.
We explore the asymmetric Einstein-Podolsky-Rosen (EPR) steering of field modes via atomic coherent effects. A resonant four-level system in double-cascade configuration is under our consideration, where the atoms are excited by the applied fields from one cascade channel and two cavity modes are generated from the other cascade transition. The results show two cavity modes are suitable for achieving the steady-state one-way EPR steering. We analyze the physics in terms of the dressed-atom Bogoliubov-field-mode approach. It is found that one of two Bogoliubov modes is mediated by the resonant coupling of the dressed atoms and the other is decoupled from them. This leads to the so-called one-channel dissipation, by which the dressed atoms absorb the average excitations from one transformed mode and then two original modes are pulled into the asymmetric correlation. Remarkably, the present scheme is focused on the full-resonant interaction not only between the classical fields, the cavity modes and the bare atoms, but also between the Bogoliubov modes and dressed atoms, which will induce the one-way steering simply via adjusting the intensity of an external field. Furthermore, the EPR steering could occur between the field modes with the large frequency difference, such as optical and microwave fields, which is more useful for the practical quantum communication. Based on the one-channel dissipation, the obtainable one-way EPR steering is rather against the dynamic fluctuations and is regardless of the initial state.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlation that exhibits a fundamental asymmetry in the properties of quantum systems. Given two observers, Alice and Bob, there are known to exist bipartite entangled states which are one-way steerable in the sense that Alice can steer Bob's state, but Bob cannot steer Alice's state. Here, we generalize this phenomenon to three parties and find a cyclic property of tripartite EPR steering. In particular, we identify a three-qubit state whose reduced bipartite states are one-way steerable for arbitrary projective measurements. Moreover, the three-qubit state has a cyclic steering property in the sense that by arranging the system in a triangular configuration the neighboring parties can steer each other's states only in the same (e.g., clockwise) direction. That is, Alice can steer Bob's state, Bob can steer Charlie's state, and Charlie can steer Alice's state, but not the other way around.