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Journal of Physics B Atomic Molecular and Optical Physics

Negative temperature phenomena in two coupled qubit-ensembles

Yuxiang Han, Xin Wang, Hongrong Li

Published May 17, 2022• 0 citations
Publisher

Abstract

Abstract Negative absolute temperature has a wide range of applications, such as high-efficiency quantum heat engines, quantum refrigerators, and quantum simulation. In a recent paper (2018 Phys. Rev. Lett. 120 060403), the authors proposed two spin ensembles coupled to the same reservoir collectively; one ensemble relaxes to negative temperature since the two ensembles have unbalanced spin sizes. However, the coherent coupling mediated by the common environment is not considered. Here, we discuss negative temperature in a system where two qubit-ensembles are coupled to the same 1D waveguide. In the limit of Markovian approximation, by investigating the coherent coupling and non-cross (cross) collective decay between two qubit-ensembles, we find that the duration of the negative temperature state depends on the distance between the two ensembles. The decrease in negative temperature duration is due to the coherent coupling between the two ensembles that will hybridize the unitary evolution of the system. Some optimal points produce the longest duration of negative temperature, but this could not occur since the distance is out of the range of the appropriate regions. The negative temperature subensemble plays the role of a reservoir in the quantum Otto heat engine, which takes place beyond the Otto limit.

DOI
10.1088/1361-6455/ac7095

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Abstract Negative absolute temperature has a wide range of applications, such as high-efficiency quantum heat engines, quantum refrigerators, and quantum simulation. In a recent paper (2018 Phys. Rev. Lett. 120 060403), the authors proposed two spin ensembles coupled to the same reservoir collectively; one ensemble relaxes to negative temperature since the two ensembles have unbalanced spin sizes. However, the coherent coupling mediated by the common environment is not considered. Here, we discuss negative temperature in a system where two qubit-ensembles are coupled to the same 1D waveguide. In the limit of Markovian approximation, by investigating the coherent coupling and non-cross (cross) collective decay between two qubit-ensembles, we find that the duration of the negative temperature state depends on the distance between the two ensembles. The decrease in negative temperature duration is due to the coherent coupling between the two ensembles that will hybridize the unitary evolution of the system. Some optimal points produce the longest duration of negative temperature, but this could not occur since the distance is out of the range of the appropriate regions. The negative temperature subensemble plays the role of a reservoir in the quantum Otto heat engine, which takes place beyond the Otto limit.
Spin collective phenomena including superradiance are even today being intensively investigated with experimental tests performed based on state-of-the-art quantum technologies. Such attempts are not only for the simple experimental verification of predictions from the last century, but also as a motivation to explore new applications of spin collective phenomena and the coherent control of the coupling between spin ensembles and reservoirs. In this paper, we investigate the open quantum dynamics of two spin ensembles (double-spin domains) coupled to a common bosonic reservoir. We analyze in detail the dynamics of our collective state and its structure by focusing on both the symmetry and asymmetry of this coupled spin system. We find that when the spin size of one of the double domains is larger than that of the other domain, at the steady state this system exhibits two unusual collective behaviors: the negative-temperature-state relaxation in the smaller spin domain and the reservoir-assisted quantum entanglement between the two domains. These results are the consequence of the asymmetry of this system and the decoherence driven by the common reservoir.
The engineering of quantum systems and their environments has led to our ability now to design composite or complex systems with the properties one desires. In fact, this allows us to couple two or more distinct systems to the same environment where potentially unusual behavior and dynamics can be exhibited. In this Letter we investigate the relaxation of two giant spins or collective spin ensembles individually coupled to the same reservoir. We find that, depending on the configuration of the two individual spin ensembles, the steady state of the composite system does not necessarily reach the ground state of the individual systems, unlike what one would expect for independent environments. Further, when the size of one individual spin ensemble is much larger than the second, collective relaxation can drive the second system to an excited steady state even when it starts in the ground state; that is, the second spin ensemble relaxes towards a negative-temperature steady state.
We perform an experiment in which a quantum heat engine works under two reservoirs, one at a positive spin temperature and the other at an effective negative spin temperature, i.e., when the spin system presents population inversion. We show that the efficiency of this engine can be greater than that when both reservoirs are at positive temperatures. We also demonstrate the counterintuitive result that the Otto efficiency can be beaten only when the quantum engine is operating in the finite-time mode.
Cyclic classical and quantum thermal machines show higher efficiency when the strokes are carried out quasi-statically. Recent theoretical and experimental work on figures of merit for thermal machines show that they have an advantage when operating in environments with negative temperatures. In an experimental proof of concept [Phys. Rev. Lett. 122, 240602 (2019)], it was shown that quantum Otto engines operating at negative temperatures can exhibit a behavior in which the faster the cycle is carried out, the higher the efficiency. In this work, we make use of the concept of entropy production and friction work to explain this counterintuitive behavior, and we show that it only occurs when reservoirs have negative temperatures.
Abstract This paper proposes a theoretical model for a heat engine operating on the Otto cycle, employing a two-qubit Heisenberg chain as its working substance. This system is subjected to an external, time-dependent homogeneous magnetic field and a symmetric cross-spin interaction. The interaction is configured to occur along two distinct orientations, contingent upon the direction of Zeeman energy and symmetric interaction: either exclusively along the X -direction or exclusively along the Z -direction. Furthermore, the thermal reservoirs integral to the Otto engine are considered to engage with the working substance via two discrete modes: a localized interaction or a collective interaction. The two qubits exhibit weak coupling to a non-equilibrium thermal environment during the isochoric heating and cooling strokes, thereby validating the application of a Markovian model as a suitable approximation for describing the time evolution of the working substance. This study investigates the influence of various system parameters on the thermodynamic quantities and the resultant power output. A principal finding is that refrigeration functionality is the predominant operational characteristic when the system engages in collective interaction with the reservoirs. Conversely, localized interactions facilitate dual operational modes, with the sign of the Zeeman energy determining the function as either a refrigerator or a heat engine. Significantly, positive power output is achieved in the engine regime, and we find that the choice of interaction axis acts as a powerful amplification mechanism for the thermodynamic output, while the system-environment coupling scheme proves to be the most decisive factor in determining the machine’s fundamental purpose.
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.