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Revista Mexicana de Física

Schroedinger’s cat states generated by the environment

D. D. Bhaktavatsala Rao, Nir Bar‐Gill, Gershon Kurizki

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

"As a rule, the coupling of a quantum system to an uncontrollable thermal reservoir (a “bath”) gives rise to the system’s decoherence, i.e., the destruction of its unitary coherent evolution [1]. Not less common is the rule that the more complex the quantum system, the more detrimental are the bath effects [2]. Here we point out that the coupling of a complex quantum system to a bath may actually induce advantageous coherent dynamics. Namely, an exact solution for a quantum many-body system characterized by large angular momentum (or spin) that is coupled to a thermal bath reveals a hitherto unexplored general effect: bath-induced effectively nonlinear evolution. This evolution can drive the large-spin system into a macroscopic quantum-superposition (“Schroedinger-cat”) state [3, 4]. Such counter-intuitive bath-induced effects should be observable in various setups on long (Markovian) time scales. They change our perspective of non-classicality in open many-body quantum systems. Namely, the bath may cause rather than impede the formation of distinctly non-classical Schroedinger-cat states, despite their fragility in the presence of a bath [2, 5]."

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"As a rule, the coupling of a quantum system to an uncontrollable thermal reservoir (a “bath”) gives rise to the system’s decoherence, i.e., the destruction of its unitary coherent evolution [1]. Not less common is the rule that the more complex the quantum system, the more detrimental are the bath effects [2]. Here we point out that the coupling of a complex quantum system to a bath may actually induce advantageous coherent dynamics. Namely, an exact solution for a quantum many-body system characterized by large angular momentum (or spin) that is coupled to a thermal bath reveals a hitherto unexplored general effect: bath-induced effectively nonlinear evolution. This evolution can drive the large-spin system into a macroscopic quantum-superposition (“Schroedinger-cat”) state [3, 4]. Such counter-intuitive bath-induced effects should be observable in various setups on long (Markovian) time scales. They change our perspective of non-classicality in open many-body quantum systems. Namely, the bath may cause rather than impede the formation of distinctly non-classical Schroedinger-cat states, despite their fragility in the presence of a bath [2, 5]."
Abstract By virtue of the superoperator technique, we solve analytically the non-Markovian master equation that describes single-mode continuous variable system interacting with a structure reservoir. Our analytical solution allows us to investigate the non-Markovian effects on the dynamics of quantum coherence and non-classicality of Schrödinger cat states embedded in various types of structured reservoirs. We show that the dynamical behaviors of the fidelity, entanglement potentials, and higher-order antibunching of such states can be divided into two phases: they decay rapidly within a short time, but would either vanish completely or tend to a nonzero steady-state value in the long-time limit depending on the initial Schrödinger cat states and system parameters. We also show that by examining the Wigner function and higher-order sub-Poissonian statistics, the super-Ohmic environment can better help to protect the non-classicality, whereas the sub-Ohmic environment causes the disappearance of the non-classicality. Our approach is concise and can generalize to other open quantum system coupled to non-Markovian environment at finite-temperature or to linear non-Markovian Gaussian system.
Quantum decoherence in all its locus of essence, and expression is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. Detrimental ramifications, and pernicious implications of this dephasing leads to classical or probabilistically additive behavior. Quantum decoherence gives the appearance of wave function collapse (the reduction of the physical possibilities into a single possibility as seen by an observer. Here it is to be noted that perception is not the reality and what you see is not what you see ;what you do not see is what you do not see; what you see is what you do not see ;and what you do not see is what you see.)… Thus in all its wide ranging manifestations, it justifies the propositional subsistence and corporeal reality that justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges out of a perceptual field   of quantum starting point and it determines the location of the quantum-classical boundary. Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents transitive states, substantive sub states and determinate orientation different elements in the quantum superposition of the system and environment's wavefunction from interfering with each other. Decoherence has been a subject of active research since the 1980s. Decoherence can be viewed as the principal frontier of diurnal dynamics that results in loss of information from a system into the environment (often modeled as a heat bath), since every system is loosely coupled with the energetic state of its surroundings, with particularistic predicational pronouncements. . Viewed in isolation, the system's dynamics are non-unitary (although the combined system plus environment evolves in a unitary fashion). Thus, the dynamics of the system aphorism and anecdote of the system alone are irreversible. As with any coupling, entanglements are generated in its theme and potentialities between the system and environment, which have the effect of sharing quantum information with—or transferring it to—the surroundings. It is a blatant and flagrant misconception that collapse of wave function is attributable and ascribable to wave function collapse; Decoherence does not generate actual wave function collapse. It only provides an explanation for the appearance of the wavefunction collapse, as the quantum nature of the system leaks into the environment. So, the wave function collapse is the figment of the observer’s imagination, product of puerile prognostication and resultant orientationality of his phantasmagoria.  One cannot have the apodictic knowledge of reality that is; components of the wavefunction are decoupled from a coherent system, and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue. This is a very important pharisaical provenience and plagenetious precocity with all the disembodied resemblances of the system in total form; specifically, decoherence does not attempt to explain the measurement problem. Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive. Moreover, our observation tells us that this mixture looks like a proper quantum ensemble in a measurement situation, as we observe that measurements lead to the of precisely one state in the ensemble.Decoherence represents a challenge for the practical realization of quantum computers, since they are expected to rely heavily on the undisturbed evolution of quantum coherences. Simply put; they require that coherent states be preserved and that decoherence is managed, in order to actually perform quantum computation. In the following we give a model for decoherence of the environment, coupled quantum states, at determinate and differential levels ,internal resonance in coupled spin systems, and the conflict in the Quantum state operations and decoupling. KEY WORDS Coupled quantum states, Quantum mechanics
The unavoidable interaction of a quantum system with its surrounding environment (its bath) is not always detrimental for quantum properties. For instance, under some specific conditions (that we identify as indistinguishability), a many-body system can gain internal coherences thanks to the interaction with its bath. The most famous consequence of this phenomenon is super-radiance. Beyond that, the thermodynamic effects on the system of these bath-induced coherences have been mostly unexplored. We show here, for a simple and common system (a pair of two-level systems), that the energetic and entropic impacts can indeed be dramatic and diverse, including amplification of the action of the bath but also its mitigation. Our results can be tested experimentally. They suggest that bath-induced coherences can be harnessed to enhance thermodynamic tasks, opening up interesting perspectives for thermal machines, quantum battery charging, natural or artificial energy harvesting systems, and state preparation and protection.
Thermalization in open systems coupled to macroscopic environments is usually analyzed from the perspective of relaxation of the reduced state of the system to the equilibrium state. Less emphasis is given to the change of the state of the bath. However, as previously shown for some specific models, during the thermalization the environment may undergo a nontrivial dynamics, indicated by the the change of its von Neumann entropy, at timescales even longer than the relaxation time of the system; here such a behavior is called post-thermalization. We provide a more detailed analysis of this phenomenon by simulating the full dynamics of a variety of systems together with their environment. In particular, the post-thermalization is qualitatively explained as a result of reconversion of the initially built up correlation between the system and the bath into the correlation between the degrees of freedom in the environment. We also present exemplary systems in which such a reconversion is suppressed due to non-Markovian dynamics or the presence of interactions.
During the past decade, the experimental development of being able to create ever larger and heavier quantum superpositions has brought the discussion of the connection between microscopic quantum mechanics and macroscopic classical physics back to the forefront of physical research. Under equilibrium conditions this connection is in fact well understood in terms of the mechanism of spontaneous symmetry breaking, while the emergence of classical dynamics can be described within an ensemble averaged description in terms of decoherence. The remaining realm of individual-state quantum dynamics in the thermodynamic limit was addressed in a recent paper proposing that the unitarity of quantum mechanical time evolution in macroscopic objects may be susceptible to a spontaneous breakdown. Here we will discuss the implications of this theory of spontaneous unitarity breaking for the modern experiments involving truly macroscopic Schrodinger cat states.