The decoherence of a qubit coupled with the phonons of a finite-size lattice is investigated. The confined phonons no longer behave as a reservoir. They remain sensitive to the qubit so that the origin of the decoherence is twofold. First, a qubit-phonon entanglement yields an incomplete true decoherence. Second, the qubit renormalizes the phonon frequency resulting in fake decoherence when a thermal average is performed. To account for the initial thermalization of the lattice, the qua- ntum Langevin theory is applied so that the phonons are viewed as an open system coupled with a thermal bath of harmonic oscillators. Consequently, it is shown that the finite lifetime of the phonons does not modify fake decoherence but strongly affects true decoherence. Depending on the values of the model parameters, the interplay between fake and true decoherence yields a very rich dynamics with various regimes.
The decoherence of a qubit coupled with the phonons of a finite-size lattice is investigated. The confined phonons no longer behave as a reservoir. They remain sensitive to the qubit so that the origin of the decoherence is twofold. First, a qubit-phonon entanglement yields an incomplete true decoherence. Second, the qubit renormalizes the phonon frequency resulting in fake decoherence when a thermal average is performed. To account for the initial thermalization of the lattice, the qua- ntum Langevin theory is applied so that the phonons are viewed as an open system coupled with a thermal bath of harmonic oscillators. Consequently, it is shown that the finite lifetime of the phonons does not modify fake decoherence but strongly affects true decoherence. Depending on the values of the model parameters, the interplay between fake and true decoherence yields a very rich dynamics with various regimes.
The exciton-phonon system in a confined environment is revisited within standard perturbation theory. Special attention is paid to describing the time evolution of the excitonic coherences at finite temperature. To proceed, the system involving an exciton dressed by a single phonon mode is considered. Owing to its simplicity, it is solved exactly so that the relevance of the perturbation theory is checked. Within the nonadiabatic weak-coupling limit, it is shown that several time scales govern the coherence dynamics. In the short-time limit, the coherences behave as if the exciton was insensitive to the phonon bath. Then, quantum decoherence takes place. Finally the coherences recur almost periodically at specific revival times. Coherence decay and revival strongly depend on the nature of the excitonic states. In particular, for odd lattice sizes, the coherence of the state exactly located at the band center survives over a very long-time scale. Therefore, confinement-induced decoherence softening favors high-fidelity quantum-state transfer and allows to encode the information on a quantum bit almost insensitive to quantum decoherence.
We study theoretically the phonon-induced relaxation and decoherence processes in the hybrid qubit in silicon. A hybrid qubit behaves as a charge qubit when the detuning is close to zero and as a spin qubit for large detuning values. It is realized starting from an electrostatically defined double quantum dot where three electrons are confined and manipulated through only electrical tuning. By employing a three-level effective model for the qubit and describing the environment bath as a series of harmonic oscillators in the thermal equilibrium states, we extract the relaxation and decoherence times as a function of the bath spectral density and of the bath temperature using the Bloch-Redfield theory. For Si quantum dots the energy dispersion is strongly affected by the physics of the valley, i.e., the conduction band minima, so we also included the contribution of the valley excitations in our analysis. Our results offer fundamental information on the system decoherence properties when the unavoidable interaction with the environment is included and temperature effects are considered.
The intention of this work is twofold: first, to present a most simple system capable of simulating the intrinsic bosonic Josephson effect with photons and, second, to study various outcomes deriving from inherent or external decoherence. A qubit induces an effective coupling between two externally pumped cavity modes. Without cavity losses and in the dispersive regime, intrinsic Josephson oscillations of photons between the two modes occurs. In this case, contrary to regular Markovian decoherence, the qubit purity shows a Gaussian decay and recurrence of its coherence. Due to intrinsic nonlinearities, both the Josephson oscillations as well as the qubit properties display a rich collapse-revival structure, where, however, the complexity of the qubit evolution is in some sense stronger. The qubit as a meter of the photon dynamics is considered, and it is shown that qubit dephasing, originating, for example, from nondemolition measurements, results in an exponential destruction of the oscillations which manifests the collectiveness of the Josephson effect. Nonselective qubit measurements, on the other hand, render a Zeno effect seen in a slowing down of the Josephson oscillations. Contrary to dephasing, cavity dissipation results in a Gaussian decay of the scaled Josephson oscillations. Finally, following Ponomarev et al. [Phys. Rev. Lett. 106, 010405 (2011)], we analyze aspects of thermalization. In particular, despite similarities with the generic model studied by Ponomarev et al., our system does not seem to thermalize.
The dynamics of charge qubits coupled to a nanomechanical resonator under influence of both a phonon bath in contact with the resonator and irreversible decay of the qubits is considered. The focus of our analysis is devoted to multi partite entanglement and the effects arising from the coupling to the reservoir. It is shown that despite losses, entanglement formation may still persist for relatively long times and it is especially robust against temperature dependence of the reservoir. Together with control of system parameters, the system may therefore be especially suited for quantum information processing. Furthermore, our results shed light on the evolution of open quantum many-body systems. For instance, due to intrinsic qubit-qubit couplings our model is related to a driven XY spin model.
We analyze the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The chain mediates interactions between the qubits and acts as a non-Markovian reservoir. The model is amenable to an analytical solution when the initial state of the chain is Gaussian. We study the dynamics of the qubits' concurrence starting from a separable state and assuming that the chain spectrum is gapped and the chain is initially in a thermal state. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak-coupling regime, where the qubits are entangled at the asymptotics, (ii) the strong-coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude, and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitations. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits' distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study unravels the basic mechanisms leading to entanglement in a non-Markovian bath and allows one to identify the key resources for realizing quantum coherent dynamics of open systems.
The study of entanglement has gained prominence in recent years due to the advent of fields such as Quantum Optics and Quantum Information Theory — advances that have harnessed such counter-intuitive quantum phenomena into elements of everyday life, improving it in the process. Ideal quantum systems, “closed” to the outside world, remain quantum forever and thus manage to retain entanglement. Real quantum systems, however, are “open” to the environment and are therefore susceptible to the phenomenon of decoherence. The resultant loss of entanglement is a major hindrance to the effectiveness of quantum information tasks. In this thesis we have studied the evolution of entanglement in various types of open quantum systems (OQS) coupled in various ways to local baths. We have also studied existing ways and means of controlling the decay of entanglement and have proposed a new method of doing so. We have studied the evolution of entanglement in OQS undergoing Markovian dynamics by using the Lindblad master equation as well as the method of quantum trajectories. We have analyzed the onset of the phenomenon of entanglement sudden death in finite as well as infinite dimensional OQS, connected either locally to a thermal bath or its squeezed variant, or via a quantum non-demolition-type (QND-type) interaction to a local thermal bath. We have found that the QND-type system-bath interaction works best to conserve entanglement in finite dimensional systems, whereas a squeezed thermal bath causes entanglement sudden death even at zero temperature. We have also studied some well-known methods of controlling decoherence in open systems with respect to their ability of preserving entanglement. Some of these procedures include coupling the system to a thermal bath of photonic crystals where the photonic band gap suppresses decoherence, modulation of the systembath frequency in an attempt to contain decoherence, using the method of resonance fluorescence where an external field modulates the transition frequency of the two-qubit systems with each qubit being a two-state atomic system to contain decoherence, and using high-frequency radio waves to decouple the system and bath dynamically and thus reducing decoherence. Our study has revealed a rather startling fact — some of these decoherence control procedures actually result in an elevated rate of loss and a resultant quicker death of entanglement. This is a 6 surprising and extremely counter-intuitive result. Finally, we have proposed a new method of shielding the entanglement in the system from dissipative environmental effects. In this procedure, an ancillary system in a fixed initial state is allowed to interact with the main system through exchange interactions. We have, through numerical computation, showed that an ancilla in the ground state extends the lifespan of entanglement in the main system. Increasing the size of the ancilla, that is, increasing the value of n in an n-qubit ancilla slows down entanglement loss for a two-qubit system connected locally to a thermal bath.