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arXiv:1905.07604 · Journal of the Optical Society of America B

Entanglement dynamics of moving qubits in a common environment

Sare Golkar, Mohammad Kazem Tavassoly, Alireza Nourmandipour

Published Dec 23, 2019• 19 citations
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Abstract

In this paper, we provide an analytical investigation of the entanglement dynamics of moving qubits dissipating into a common and (in general) non-Markovian environment for both weak and strong coupling regimes. We first consider the case of two moving qubits in a common environment and then generalize it to an arbitrary number of moving qubits. Our results show that when the system evolves from an initial entangled state, the amount of initial entanglement decreases and finally disappears after a finite interval of time due to the environmental effects. Moreover, we observe that the movement of qubits has a constructive role in the protection of the initial entanglement. In a sense, in this case, we observe a Zeno-like effect due to the velocity of qubits. On the other hand, we demonstrate how a stationary state of entanglement may be achieved when we consider the case in which at least one of the moving qubits is initially in the ground state. Surprisingly, we observe that when we extend the number of moving qubits with the same velocity, the stationary state of the qubits does not depend on the velocity of qubits as well as on the environmental properties. This means that, in this condition, the stationary state of entanglement depends only on the number of moving qubits.

DOI
10.1364/josab.379261

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In this paper, we provide an analytical investigation of the entanglement dynamics of moving qubits dissipating into a common and (in general) non-Markovian environment for both weak and strong coupling regimes. We first consider the case of two moving qubits in a common environment and then generalize it to an arbitrary number of moving qubits. Our results show that when the system evolves from an initial entangled state, the amount of initial entanglement decreases and finally disappears after a finite interval of time due to the environmental effects. Moreover, we observe that the movement of qubits has a constructive role in the protection of the initial entanglement. In a sense, in this case, we observe a Zeno-like effect due to the velocity of qubits. On the other hand, we demonstrate how a stationary state of entanglement may be achieved when we consider the case in which at least one of the moving qubits is initially in the ground state. Surprisingly, we observe that when we extend the number of moving qubits with the same velocity, the stationary state of the qubits does not depend on the velocity of qubits as well as on the environmental properties. This means that, in this condition, the stationary state of entanglement depends only on the number of moving qubits.
We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting of an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak- and strong-coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of nonselective measurements can protect the relevant entanglement. On the other hand, by limiting the number of qubits initially in the superposition of single excitation, a stationary entanglement can be created between qubits initially in the excited and ground states. Finally, we determine the stationary distribution of the entanglement versus the total number of qubits in the system.
Abstract Efficient entanglement preservation in open quantum systems is a crucial scope towards a reliable exploitation of quantum resources. We address this issue by studying how two-qubit entanglement dynamically behaves when two atom qubits move inside two separated identical cavities. The moving qubits independently interact with their respective cavity. As a main general result, we find that under resonant qubit-cavity interaction the initial entanglement between two moving qubits remains closer to its initial value as time passes compared to the case of stationary qubits. In particular, we show that the initial entanglement can be strongly protected from decay by suitably adjusting the velocities of the qubits according to the non-Markovian features of the cavities. Our results supply a further way of preserving quantum correlations against noise with a natural implementation in cavity-QED scenarios and are straightforwardly extendable to many qubits for scalability.
We provide an analytical investigation of the entanglement dynamics for a system composed of an arbitrary number of qubits dissipating into a common environment. Specifically, we consider product initial states with a given number of excitations whose evolution remains confined on low-dimensional subspaces of the operators space. We then find for which pairs of qubits entanglement can be generated and can persist at a steady state. Finally, we determine the stationary distribution of entanglement as well as its scaling versus the total number of qubits in the system.
We propose a scheme to generate entanglement between two distant qubits (two-level atom) which are separately trapped in their own (in general) non-Markovian dissipative cavities by utilizing entangling swapping, considering the case in which the qubits can move along their cavity axes rather than a static state of motion. We first examine the role of movement of the qubit by studying the entropy evolution for each subsystem. The average entropy over the initial states of the qubit is calculated. Then by performing a Bell state measurement on the fields leaving the cavities, we swap the entanglement between qubit-field in each cavity into qubit-qubit and field-field subsystems. The entangling power is used to measure the average amount of swapped entanglement over all possible pure initial states. Our results are presented in two weak and strong coupling regimes, illustrating the positive role of movement of the qubits on the swapped entanglement. It is revealed that by considering certain conditions for the initial state of qubits, it is possible to achieve a maximally long-leaving stationary entanglement (Bell state) which is entirely independent of the environmental variables as well as the velocity of qubits. This happens when the two qubits have the same velocities.
We investigate the quantum Zeno and anti-Zeno effects on pairwise entanglement dynamics of a collective of noninteracting qubits which have been initially prepared in a Werner state and are off-resonantly coupled to a common and non-Markovian environment. We obtain the analytical expression of the concurrence in the absence and presence of the nonselective measurements. In particular, we express our results in the strong and weak coupling regimes and examine the role of the system size and the effect of the detuning from the cavity field frequency on the temporal behavior of the pairwise entanglement. We show that the detuning parameter has a positive role in protection of entanglement in the absence of the measurement for the weak coupling regime. We find that for the values of detuning parameter less than the cavity damping rate, the quantum Zeno effect is always dominant, while for values greater than the cavity damping rate, both Zeno and anti-Zeno effects can occur, depending on the measurement intervals. We also find that the anti-Zeno effect can occur in the pairwise entanglement dynamics in the absence and presence of the detuning in the strong coupling regime.
In this paper, we consider the entanglement dynamics of two identical qubits (two-level atoms) accompanied by dipole–dipole interaction within a common reservoir in the strong and weak coupling regimes. We suppose that the qubits move in the reservoir which is at zero temperature. Using the time-dependent Schrödinger equation, the state vector of the qubits-reservoir system is obtained by which we can evaluate the concurrence as a suitable measure of entanglement between the two qubits. The results show that by choosing special initial conditions for the qubits, a different dynamical behavior of entanglement is visible in such a way that entanglement protection occurs. Also, we find that the qubit motion in the absence of dipole–dipole interaction leads to preservation or at least more slowly decay of entanglement. However, in the presence of dipole–dipole interaction with the movement of qubits, different results can be observed which depend on the initial states of the qubits, i.e. entanglement may or may not be protected.