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Physical Review A

Fast creation of entanglement by interaction with a common bath

Nan Qiu, Xiang‐Bin Wang

Published Dec 26, 2013• 3 citations
Publisher

Abstract

We propose a scheme to quickly create a conditional quantum phase shift and quantum entanglement of two qubits interacting with a common heat bath. Dynamic decoupling is applied in the scheme so that it works even in the regime of strong interaction between the qubits and the environment. Our scheme does not require any direct interaction between the two qubits.

DOI
10.1103/physreva.88.062332

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We propose a scheme to quickly create a conditional quantum phase shift and quantum entanglement of two qubits interacting with a common heat bath. Dynamic decoupling is applied in the scheme so that it works even in the regime of strong interaction between the qubits and the environment. Our scheme does not require any direct interaction between the two qubits.
I show that entanglement between two qubits can be generated if the two qubits interact with a common heat bath in thermal equilibrium, but do not interact directly with each other. In most situations the entanglement is created for a very short time after the interaction with the heat bath is switched on, but depending on system, coupling, and heat bath, the entanglement may persist for arbitrarily long times. This mechanism sheds new light on the creation of entanglement. A particular example of two quantum dots in a closed cavity is discussed, where the heat bath is given by the blackbody radiation.
We solve the time evolution for most general density matrix for 2‐qubits under the interaction with a common heat bath and investigate the time evolution for a particularly interesting entangled state where we provide a scheme to enhance or concentrate entanglement using common heat bath interaction. The correspondence between the entanglement dynamics and energy exchange of the system with the environment is discussed under that situation. Entanglement sudden death, decoherence free entanglement and entanglement enhancement are shown to be dependent on the energy exchange of the system with the environment.
It has recently been shown that interactions among the spins of a bath can result in an effective suppression of the decoherence of a single qubit embedded in a multi-spin environment. However, the effects of such intrabath interaction on the dynamics of entanglement are still not well understood. Here we study the dynamics of a system composed of two entangled qubits coupled to (1) independent self-interacting spin baths, and (2) a common self-interacting spin bath. We find that, as in the case of a single qubit, strong interactions among the spins in the bath may induce an effective decoupling between the bath and the system—this in turn suppresses the loss of entanglement that a non-, or weakly, interacting bath would typically cause. However we find that the intrabath interaction strength needed to achieve such effects is much larger than in the single qubit case, especially when the two qubits share the same environment. Our results illustrate the system's size effects in the entanglement sharing condition, where the entanglement within the bath limits the entanglement between the bath and the system.
We study the steady-state entanglement and heat current of two coupled qubits, in which two qubits are connected with two independent heat baths (IHBs) or two common heat baths (CHBs). We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steady-state with stronger coupling regime between two qubits than qubit–baths. We do not make the rotating wave approximation (RWA) for the qubit–qubit interaction, and so we are able to investigate the behaviors of the system in both the strong coupling regime and the weak coupling regime, respectively. In an equilibrium bath, we find that the entanglement decreases with the bath temperature and energy detuning increasing under the strong coupling regime. In the weak coupling regime, the entanglement increases with coupling strength increasing and decreases with the bath temperature and energy detuning increasing. In a nonequilibrium bath, the entanglement without RWA is useful for entanglement at lower temperatures. We also study the heat currents of the two coupled qubits and their variations with the energy detuning, coupling strength and low temperature. In the strong (weak) coupling regime, the heat current increases (decreases) with coupling strength increasing when the temperature of one bath is lower (higher) than the other, and the energy detuning leads to a positive (negative) effect when the temperature is low (high). In the weak coupling regime, the variation trend of heat current is opposite to that of coupling strength for the IHB case and the CHB case.
We investigate how two spatially separated qubits coupled to a common heat bath can be entangled by purely dissipative dynamics. We identify a dynamical time scale associated with the lifetime of the dissipatively generated entanglement and show that it can be much longer than either the typical single-qubit decoherence time or the time scale on which a direct exchange interaction can entangle the qubits. We give an approximate analytical expression for the long-time evolution of the qubit concurrence and propose an ion trap scheme in which such dynamics should be observable.