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Canadian Journal of Chemistry

Can quantum control modify thermodynamic behavior?

David Gelbwaser-Klimovsky, Noam Erez A, Robert Alicki, Gershon Kurizki

Published Oct 12, 2013• 2 citations
Publisher

Abstract

We review the effects of frequent, impulsive quantum nondemolition measurements of the energy of two-level systems, alias qubits, in contact with a thermal bath. The resulting entropy and temperature of the system subject to measurements at intervals below the bath memory (Markovianity) time are completely determined by the measurement rate. Namely, they are unrelated to what is expected by standard thermodynamical behavior that holds for Markovian baths. These anomalies allow for very fast control of heating, cooling, and state-purification (entropy reduction) of qubits, much sooner than their thermal equilibration time. We further show that frequent measurements may enable the extraction of work in a closed cycle from the system−bath interaction (correlation) energy, a hitherto unexploited work resource. They allow for work even if no information is gathered or the bath is at zero temperature, provided the cycle is within the bath memory time.

DOI
10.1139/cjc-2013-0327

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We review the effects of frequent, impulsive quantum nondemolition measurements of the energy of two-level systems, alias qubits, in contact with a thermal bath. The resulting entropy and temperature of the system subject to measurements at intervals below the bath memory (Markovianity) time are completely determined by the measurement rate. Namely, they are unrelated to what is expected by standard thermodynamical behavior that holds for Markovian baths. These anomalies allow for very fast control of heating, cooling, and state-purification (entropy reduction) of qubits, much sooner than their thermal equilibration time. We further show that frequent measurements may enable the extraction of work in a closed cycle from the system−bath interaction (correlation) energy, a hitherto unexploited work resource. They allow for work even if no information is gathered or the bath is at zero temperature, provided the cycle is within the bath memory time.
We study deviations from thermal equilibrium between two-level systems (TLS) and a bath by frequent and brief quantum measurements of the TLS energy-states. The resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for Markovian baths. These anomalies allow for very fast control heating, cooling and state-purification (entropy reduction) of quantum systems much sooner than their thermal equilibration time.
We study disturbances of thermal equilibrium between two-level systems (TLS) and a bath by frequent and brief quantum measurements of the TLS energy-states. If the measurements induce either the Zeno or the anti-Zeno regime, namely, the slowdown or speedup of the TLS relaxation, then the resulting entropy and temperature of both the system and the bath are found to be completely determined by the measurement rate, and unrelated to what is expected by standard thermodynamical rules that hold for markovian baths. These anomalies allow for very fast control heating, cooling and state-purification (entropy reduction) of quantum systems much sooner than their thermal equilibration time.
We show that frequent nondemolition measurements of a quantum system immersed in a thermal bath allow the extraction of work in a closed cycle from the system-bath interaction (correlation) energy, a hitherto unexploited work resource. It allows for work even if no information is gathered or the bath is at zero temperature, provided the cycle is within the bath memory time. The predicted work resource may be the basis of quantum engines embedded in a bath with long memory time, such as the electromagnetic bath of a high-QQQ cavity coupled to two-level systems.
Quantum two-state systems, known as quantum bits (qubits), are unavoidably in contact with their uncontrolled thermal environment, also known as a macroscopic 'bath'. The higher the temperature of the qubits, the more impure their quantum state and the less useful they are for coherent control or quantum logic operations, hence the desirability of cooling down the qubits as much and as fast as possible, so as to purify their state prior to the desired operation. Yet, the limit on the speed of existing cooling schemes, which are all based on Markovian principles, is either the duration of the qubit equilibration with its bath or the decay time of an auxiliary state to one of the qubit states. Here we pose the conceptual question: can one bypass this existing Markovian limit? We show that highly frequent phase shifts or measurements of the state of thermalized qubits can lead to their ultrafast cooling, within the non-Markov time domain, well before they re-equilibrate with the bath and without resorting to auxiliary states. Alternatively, such operations may lead to the cooling down of the qubit to arbitrarily low temperatures at longer times. These anomalous non-Markov cooling processes stem from the hitherto unfamiliar coherent quantum dynamics of the qubit–bath interaction well within the bath memory time.
We predict [1] drastic deviations from ordinary thermodynamic trends, which are monotonic approach to thermal equilibrium and positive entropy production, when qubits coupled to bosonic baths are probed on non-Markovian time scales by quantum nondemolition measurements, as well as coherently modulated. The resulting changes in the temperature, entropy and state-purity of both the system and the bath only depend on the rate of measurement, without any rapport to thermodynamic laws. These effects in principle allow much faster cooling and state purification than other methods. Generalizations of these effects to entangled multipartite systems [2] controlled by local measurements and modulations bring about surprising dynamic changes in the entanglement. Collective bosonic states coupled to a bath are shown to obey similar principles [3].
Quantum thermodynamics explores novel thermodynamic phenomena that emerge when interactions between macroscopic systems and microscopic quantum ones go into action. Among various issues, quantum heat engines, in particular, have attracted much attention as a critical step in theoretical formulation of quantum thermodynamics and investigation of efficient use of heat by means of quantum resources. In the present paper, we focus on heat absorption and emission processes as well as work extraction processes of a quantum Otto cycle. We describe the former as non-Markovian dynamics, and thereby find that the interaction energy between a macroscopic heat bath and a microscopic qubit is not negligible. Specifically, we reveal that the interaction energy is divided into the system and the bath in a region of the short interaction time and remains negative in the region of the long interaction time. In addition, a counterintuitive energy flow from the system and the interaction energy to the hot bath occurs in another region of the short interaction time. We quantify these effects by defining an index of non-Markovianity in terms of the interaction energy. With this behavior of the interaction energy, we show that a non-Markovian quantum Otto cycle can switch functions such as an engine as well as a heater or a heat pump by controlling the interaction time with the heat bath. In particular, the qubit itself loses its energy if we shorten the interaction time, and in this sense, the qubit is cooled through the cycle. This property has a possibility of being utilized for cooling the qubits in quantum computing. We also describe the work extraction from the microscopic system to a macroscopic system like us humans as an indirect measurement process by introducing a work storage as a new reservoir.