The control of quantum entanglement in systems in contact with environment plays an important role in information processing, cryptography and quantum computing. However, interactions with the environment, even when very weak, entail decoherence in the system with consequent loss of entanglement. Here we consider a system of two coupled oscillators in contact with a common heat bath and with a time dependent oscillation frequency. The possibility to control the entanglement of the oscillators by means of an external sinusoidal perturbation applied to the oscillation frequency has been theoretically explored. We demonstrate that the oscillators become entangled exactly in the region where the classical counterpart is unstable, otherwise when the classical system is stable, entanglement is not possible. Therefore, we can control the entanglement swapping from stable to unstable regions by adjusting amplitude and phase of our external controller. We also show that the entanglement rate is approximately proportional to the real part of the Floquet coefficient of the classical counterpart of the oscillators. Our results have the intriguing peculiarity of manipulating quantum information operating on a classical system.
The control of quantum entanglement in systems in contact with environment plays an important role in information processing, cryptography and quantum computing. However, interactions with the environment, even when very weak, entail decoherence in the system with consequent loss of entanglement. Here we consider a system of two coupled oscillators in contact with a common heat bath and with a time dependent oscillation frequency. The possibility to control the entanglement of the oscillators by means of an external sinusoidal perturbation applied to the oscillation frequency has been theoretically explored. We demonstrate that the oscillators become entangled exactly in the region where the classical counterpart is unstable, otherwise when the classical system is stable, entanglement is not possible. Therefore, we can control the entanglement swapping from stable to unstable regions by adjusting amplitude and phase of our external controller. We also show that the entanglement rate is approximately proportional to the real part of the Floquet coefficient of the classical counterpart of the oscillators. Our results have the intriguing peculiarity of manipulating quantum information operating on a classical system.
Dynamical control of entanglement and its connection with the classical concept of instability is an intriguing matter which deserves accurate investigation for its important role in information processing, cryptography and quantum computing. Here we consider a tripartite quantum system made of three coupled quantum parametric oscillators in equilibrium with a common heat bath. The introduced parametrization consists of a pulse train with adjustable amplitude and duty cycle representing a more general case for the perturbation. From the experimental observation of the instability in the classical system we are able to predict the parameter values for which the entangled states exist. A different amount of entanglement and different onset times emerge when comparing two and three quantum oscillators. The system and the parametrization considered here open new perspectives for manipulating quantum features at high temperatures.
Abstract Entanglement being a foundational cornerstone of quantum sciences and the primary resource in quantum information processing, understanding its dynamical evolution in realistic conditions is essential. Unfortunately, numerous model studies show that degradation of entanglement from a quantum system’s environment, especially thermal noise, is almost unavoidable. Thus the appellation ‘hot entanglement’ appears like a contradiction, until Galve et al. [Phys. Rev. Lett. 105, 180501 (2010)] announced that entanglement can be kept at high temperatures if one considers a quantum system with time-dependent coupling between the two parties, each interacting with its individual bath. With the goal of understanding the sustenance of entanglement at high temperatures, working with the same model and set up as Galve et al, namely, parametrically-driven coupled harmonic oscillators interacting with their own Markovian baths, this work probes into the feasibility of ‘hot entanglement’ from three aspects listed in the subtitle. Our findings show that 1) hot entanglement functions only in the unstable regimes, 2) instability is a necessary but not sufficient condition, and 3) the power intake required by the drive operating in the unstable regime to sustain entanglement increases exponentially. The last factor indicates that hot entanglement under this modeling is theoretically untenable and its actual implementation likely unattainable.
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.
Abstract The tracking control of quantum correlations between two coupled qubits is analyzed, where only one of the qubits is coupled to a Markovian environment. Such a system is a generalized model that can be used, for example, to study the problem of a nuclear spin coupled to the electron spin exposed to the environment. Using an external control field, we increase the time for which the system remains coherent and entangled. The control field is an external potential applied to the system, which contains two adjustable parameters, the intensity and the phase of the field. Furthermore, we present quantum control protocols with different targets. First, for population control of both qubits, second for the coherence control of both two-level systems, and finally for the control of entanglement. Due to analytical for X states the target function can directly be identified with the entanglement. Furthermore, we have shown that when smaller dissipation rates are considered, the control method generates larger stable entanglement between the qubits.
A controllable entanglement scheme of two mechanical oscillators is proposed in a composite optomechanical system. In the case of strong driving and high dissipation, the dynamics of the movable mirror of the optomechanical cavity is characterized by an effective frequency in the long-time evolution of the system. Considering the classical nonlinear effects in an optomechanical system, we investigate the relationship between the effective frequency of the movable mirror and the adjustable parameters of the cavity. It shows that the effective frequency of the movable mirror can be adjusted ranging from ω m (the resonance frequency of the coupling oscillator) to − ω m . Under the condition of experimental realization, we can generate and control steady-state entanglement between two oscillators by adjusting the effective frequency of the movable mirror and reducing the effective dissipation by selecting the parameter of the cavity driving laser appropriately. Our scheme provides a promising platform to control the steady-state behavior of solid-state qubits using classical manipulation, which is significant for quantum information processing and fundamental research.
The physics of open quantum systems, and therefore the phenomenon of decoherence, has become important in many branches of research. Within this thesis, we investigate the system--environment interaction in the context of different problems. The influence of decoherence is ubiquitous and, due to the scale independence of quantum theory, not limited to microscopic systems. One of the great open problems in theoretical physics is the appearance of a cosmological constant which differs by many orders of magnitude from the theoretical predicted value. In the first part of this thesis we will address this question within the framework of quantum mechanics. The considerations are based on a quantum mechanical model which explains the value of the cosmological constant without introducing extremely small numbers. Decoherence, based on the uncontrollable entanglement with the environment, can explain the localization of the vacuum energy to the classical observed value. The model mentioned above allows, in principle, the tunneling into a universe with a different vacuum energy. We investigate the modification of the tunneling rate due to dissipative effects which follow from the system--bath interaction. Closely related to the cosmological constant problem and subject of the second part of this thesis is the spontaneous decay of a quantum field vacuum. Using a semiclassical approximation it is possible to investigate this process within the framework of the path integral formalism. We discuss the quantum--to--classical transition of the spontaneously nucleated vacuum bubbles. Furthermore, we investigate the dependence of the decay rate on the space-time backgrounds. The third part of this thesis is dedicated to the interaction between quantum systems and their environment in a different context. We investigate the generation of entanglement between two systems which are interacting indirectly with each other through the coupling to a heat bath. The interaction--induced entanglement will be destroyed rapidly through decoherence and dissipation. We will show that it is possible to generate a significant amount of entanglement by imposing certain boundary conditions to the bath. Furthermore, the dependence of the entanglement generation on the spatial separation of the systems will be analyzed. Specifically we will examine the bathinduced entanglement of oscillators and spins.