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Frontiers in Optics

Competition Between Incoherent Pumping and Losses in a System of Two Interacting Qubits

J.C. Triana, Karen Fonseca

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We consider a model of two qubits, which interact through a Rotating Wave Approximation (RWA) potential; while the first qubit is incoherently pumped to its excited state, the second qubit loses its excitations by contact to a zero-temperature bath. We show that purely dissipative effects (and the help of the qubit-qubit interaction) can produce entangled stationary states. The steady state entanglement is significant when the interaction constant, and the pumping and dissipation rates are of the same order of magnitude. In this toy model, the entanglement of the system exists only when the two thermal baths are on and the qubits are coupled; if we turn off either the pumping or the dissipation these correlations disappear. We calculate and compare two quantifiers of non-classical correlations: the quantum discord [3] and the entanglement of formation, in the steady state. We find an analytical form for the conditions for which the steady-state qubit-qubit entanglement attains its maximum value Css..

DOI
10.1364/fio.2017.jw4a.20

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We consider a model of two qubits, which interact through a Rotating Wave Approximation (RWA) potential; while the first qubit is incoherently pumped to its excited state, the second qubit loses its excitations by contact to a zero-temperature bath. We show that purely dissipative effects (and the help of the qubit-qubit interaction) can produce entangled stationary states. The steady state entanglement is significant when the interaction constant, and the pumping and dissipation rates are of the same order of magnitude. In this toy model, the entanglement of the system exists only when the two thermal baths are on and the qubits are coupled; if we turn off either the pumping or the dissipation these correlations disappear. We calculate and compare two quantifiers of non-classical correlations: the quantum discord [3] and the entanglement of formation, in the steady state. We find an analytical form for the conditions for which the steady-state qubit-qubit entanglement attains its maximum value Css..
The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using a recently derived Lindblad type quantum optical master equation [F. Beaudoin, J. M. Gambetta, and A. Blais, Phys. Rev. A 84, 043832 (2011)] that can describe the losses of the cavity field in a strong atom-field coupling regime. Contrary to previous investigations of the same model in the dissipative regime by using the standard Lindblad quantum optical master equation in a strong-coupling regime, the atom-field steady states are found to be cavity decay rate independent and have a very simple structure determined solely by the overlap of initial atomic state with the subradiant state which is valid for all coupling regimes. Non-RWA dynamics are found to have remarkable effects on the steady state quantum discord and entanglement that cannot be achieved under RWA conditions, for instance, they can induce steady state entanglement even for the initial states that have no overlap with the subradiant state. Moreover, the non-RWA dynamics are found to reverse the initial state dependence of steady state entanglement and quantum discord contrary to the RWA case.
The maximum entanglement allowed between two coupled qubits in the steady state established by independent incoherent sources of excitation is reported. Asymmetric configurations where one qubit is excited while the other dissipates the excitation are optimal for entanglement, reaching values three times larger than with thermal sources. The reason is the purification of the steady-state mixture (that includes a Bell state) thanks to the saturation of the pumped qubit. Photon antibunching between the cross emission of the qubits is proposed to experimentally evidence such large degrees of entanglement.
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 analytically and numerically investigate the steady-state entanglement and coherence of two coupled qubits, each interacting with a local boson or fermion reservoir, based on the Bloch-Redfield master equation beyond the secular approximation. We find that there is nonvanishing steady-state coherence in the nonequilibrium scenario, which grows monotonically with the nonequilibrium condition quantified by the temperature difference or chemical potential difference of the two baths. The steady-state entanglement, in general, is a nonmonotonic function of the nonequilibrium condition as well as the bath parameters in the equilibrium setting. We also discover that weak interqubit coupling and high base temperature or chemical potential of the baths can strongly suppress the steady-state entanglement and coherence, regardless of the strength of the nonequilibrium condition. On the other hand, the energy detuning of the two qubits, when used in a compensatory way with the nonequilibrium condition, can lead to significant enhancement of the steady-state entanglement in some parameter regimes. In addition, the qubits typically have a stronger steady-state entanglement when coupled to fermion baths exchanging particles with the system than boson baths exchanging energy with the system, under similar conditions. We also identify a close connection between the energy current flowing through the system and the steady-state coherence. Preliminary investigations suggest that these results are insensitive to the form of the reservoir spectral densities in the Markovian regime. Feasible experimental realization of measuring the steady-state entanglement and coherence is discussed for the coupled qubit system in nonequilibrium environments. Our findings offer some general guidelines for optimizing the steady-state entanglement and coherence in the coupled qubit system and may find potential applications in quantum information technology.
Dynamics of the quantum entanglement and quantum discord of two qubits in two independent baths and a common bath with the Lorentzian spectrum are studied exactly in the numerical sense within the hierarchy approach. The effects of the counter-rotating-wave terms from the system–bath coherence on these quantum correlations are systematically discussed and comparisons with previous ones under the rotating-wave approximation are also performed. For two independent baths, beyond the weak system–bath coupling, the counter-rotating-wave terms essentially change evolutions of both the entanglement and quantum discord. With increase of the coupling, revival of the entanglement after a period of complete disentanglement is suppressed dramatically and finally disappears, and the quantum discord becomes smaller monotonically. For the common bath, the entanglement is also suppressed by the counter-rotating-wave terms, but the quantum discord shows quite different behaviors if initiated from spin-correlated states. In the non-Markovian regime, the quantum discord is almost not influenced by the counter-rotating-wave terms and is generally finite in the long-time evolution at arbitrary coupling while in the Markovian regime, it is significantly enhanced with the strong coupling.
We study the dynamics of quantum correlations of two coupled double quantum dots containing two excess electrons. The dissipation is included through the contact with an oscillator bath. We solve the Redfield master equation in order to determine the dynamics of the quantum discord (QD) and the entanglement of formation (EoF). Based on our results, we find that the QD is more resistant to dissipation than the EoF for such a system. We observe that this characteristic is related to whether the oscillator bath is common to both qubits or not and to the form of the interaction Hamiltonian. Moreover, our results show that the QD might be finite, even for higher temperatures in the asymptotic limit.