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arXiv:cond-mat/0201408 · Journal of Physics A Mathematical and General

Bath-generated work extraction and inversion-free gain in two-level systems

ARMEN E. ALLAHVERDYAN, Theo M. Nieuwenhuizen

Published Jan 15, 2003• 23 citations
arXivHTMLPDF

Abstract

The spin–boson model, often used in NMR and ESR physics, quantum optics and spintronics, is considered in a solvable limit to model a spin one-half particle interacting with a bosonic thermal bath. By applying external pulses to a non-equilibrium initial state of the spin, work can be extracted from the thermalized bath. It occurs on the timescale 𝒯 2 inherent to quantum coherence. The work (partly) arises from heat given off by the surrounding bath, while the spin entropy remains constant during a pulse. This presents a new mechanism and time and temperature regimes for limiting the validity of the Clausius inequality and Thomson's formulation of the second law (cycles cost work). Apart from this, starting from a fully disordered state, coherence can be induced by employing the bath. A gain from a positive-temperature (inversion-free) two-level system is shown to be possible.

DOI
10.1088/0305-4470/36/4/301

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The spin–boson model, often used in NMR and ESR physics, quantum optics and spintronics, is considered in a solvable limit to model a spin one-half particle interacting with a bosonic thermal bath. By applying external pulses to a non-equilibrium initial state of the spin, work can be extracted from the thermalized bath. It occurs on the timescale 𝒯 2 inherent to quantum coherence. The work (partly) arises from heat given off by the surrounding bath, while the spin entropy remains constant during a pulse. This presents a new mechanism and time and temperature regimes for limiting the validity of the Clausius inequality and Thomson's formulation of the second law (cycles cost work). Apart from this, starting from a fully disordered state, coherence can be induced by employing the bath. A gain from a positive-temperature (inversion-free) two-level system is shown to be possible.
The spin‐boson model, often used in NMR and ESR physics, quantum optics and spin‐tronics, is considered in a solvable limit to model a spin one‐half particle interacting with a bosonic thermal bath. By applying external pulses to a non‐equilibrium initial state of the spin, work can be extracted from the thermalized bath. It occurs on the timescale T2 inherent to transversal (‘quantum’) fluctuations. The work (partly) arises from heat given off by the surrounding bath, while the spin entropy remains constant during a pulse. This presents a violation of the Clausius inequality and the Thomson formulation of the second law (cycles cost work) for the two‐level system.
We show that work can be extracted from a two-level system (spin) coupled to a bosonic thermal bath. This is possible due to different initial temperatures of the spin and the bath, both positive (no spin population inversion), and is realized by means of a suitable sequence of sharp pulses applied to the spin. The extracted work can be of the order of the response energy of the bath, therefore much larger than the energy of the spin. Moreover, the efficiency of extraction can be very close to its maximum, given by the Carnot bound, at the same time the overall amount of the extracted work is maximal. Therefore, we get a finite power at efficiency close to the Carnot bound. The effect comes from the back-reaction of the spin on the bath, and it survives for a strongly disordered (inhomogeneously broadened) ensemble of spins. It is connected with generation of coherences during the work-extraction process, and we deduced it in an exactly solvable model. All the necessary general thermodynamical relations are deduced from the first principles of quantum mechanics and connections are made with processes of lasing without inversion and with quantum heat engines.
The stationary state of a quantum particle strongly coupled to a quantum thermal bath is known to be non-Gibbsian, due to entanglement with the bath. For harmonic potentials, where the system can be described by effective temperatures, thermodynamic relations are shown to take a generalized Gibbsian form that may violate the Clausius inequality. For the weakly anharmonic case, a Fokker-Planck-type description is constructed. It is shown that then work can be extracted from the bath by cyclic variation of a parameter. These apparent violations of the second law are the consequence of quantum coherence in the presence of the slightly off-equilibrium nature of the bath.
Quantum mechanics describes the unitary time evolution of closed systems. In practice, every quantum system interacts with the environment leading to an irreversible loss of coherence. The Spin-Boson model (SBM) is central to the understanding of the fundamental process of decoherence of a two-state quantum system interacting with a bosonic heat bath but the nature of transient dynamics in the presence of hybrid diagonal and off-diagonal system-bath interactions remains largely unexplored. Here, we investigate how the hybrid system-bath interactions of an Ohmic environment induce localization in the bias-free SBM. For strong coupling to the environment, localization is strongly affected by a dynamically generated bias via the renormalization of the tunneling amplitude. We find that counteractive effects of Hamiltonian parameters on non-exponential short-time dynamics and long-time population equilibration can lead to a separation of timescales and non-equilibrium quantum coherent dynamics that can persist even for ultra-strong system-bath interaction. The findings offer novel opportunities to exploit coherence as a resource in quantum devices operating in the ultra-strong coupling regime.
Small quantum systems non-weakly coupled to a bath become in the quantum regime surrounded by a cloud of photons or phonons, which modifies their thermodynamic behaviour. Exactly solvable examples are the Brownian motion of a quantum particle in a harmonic confining potential and coupled to a harmonic quantum thermal bath, e.g. an ion in a Penning trap, and a spin immersed in a bosonic bath, as occurs in NMR physics. It appears that the Clausius inequality d Q≤TdS can be violated. For non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Experimental set-ups for testing some of the effects are discussed.
We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two complementary approaches, the Hierarchical Equations of Motion (HEOM) and Reaction Coordinate Mapping (RCM), are employed to examine various coupling regimes between the qubits and their respective baths. The dynamical features of the model and the impact of the tunneling amplitude on quantum coherence of the system are probed using the l1l_1l1​-norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.