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Yadin B, Imai S, Gühne O. Quantum Speed Limit for States and Observables of Perturbed Open Systems. PHYSICAL REVIEW LETTERS 2024; 132:230404. [PMID: 38905682 DOI: 10.1103/physrevlett.132.230404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Revised: 03/01/2024] [Accepted: 05/06/2024] [Indexed: 06/23/2024]
Abstract
Quantum speed limits provide upper bounds on the rate with which a quantum system can move away from its initial state. Here, we provide a different kind of speed limit, describing the divergence of a perturbed open system from its unperturbed trajectory. In the case of weak coupling, we show that the divergence speed is bounded by the quantum Fisher information under a perturbing Hamiltonian, up to an error which can be estimated from system and bath timescales. We give three applications of our speed limit. First, it enables experimental estimation of quantum Fisher information in the presence of decoherence that is not fully characterized. Second, it implies that large quantum work fluctuations are necessary for a thermal system to be driven quickly out of equilibrium under a quench. Moreover, it can be used to bound the response to perturbations of expectation values of observables in open systems.
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Das A, Mahunta S, Agarwalla BK, Mukherjee V. Precision bound and optimal control in periodically modulated continuous quantum thermal machines. Phys Rev E 2023; 108:014137. [PMID: 37583225 DOI: 10.1103/physreve.108.014137] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 07/07/2023] [Indexed: 08/17/2023]
Abstract
We use Floquet formalism to study fluctuations in periodically modulated continuous quantum thermal machines. We present a generic theory for such machines, followed by specific examples of sinusoidal, optimal, and circular modulations, respectively. The thermodynamic uncertainty relations (TUR) hold for all modulations considered. Interestingly, in the case of sinusoidal modulation, the TUR ratio assumes a minimum at the heat engine to refrigerator transition point, while the chopped random basis optimization protocol allows us to keep the ratio small for a wide range of modulation frequencies. Furthermore, our numerical analysis suggests that TUR can show signatures of heat engine to refrigerator transition, for more generic modulation schemes. We also study bounds in fluctuations in the efficiencies of such machines; our results indicate that fluctuations in efficiencies are bounded from above for a refrigerator and from below for an engine. Overall, this study emphasizes the crucial role played by different modulation schemes in designing practical quantum thermal machines.
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Affiliation(s)
- Arpan Das
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5/7, 87-100 Toruń, Poland
| | - Shishira Mahunta
- Department of Physical Sciences, Indian Institute of Science Education and Research Berhampur, Berhampur 760010, India
| | - Bijay Kumar Agarwalla
- Department of Physics, Indian Institute of Science Education and Research Pune, Pune 411008, India
| | - Victor Mukherjee
- Department of Physical Sciences, Indian Institute of Science Education and Research Berhampur, Berhampur 760010, India
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Opatrný T, Bräuer Š, Kofman AG, Misra A, Meher N, Firstenberg O, Poem E, Kurizki G. Nonlinear coherent heat machines. SCIENCE ADVANCES 2023; 9:eadf1070. [PMID: 36608121 PMCID: PMC9821940 DOI: 10.1126/sciadv.adf1070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Accepted: 12/01/2022] [Indexed: 06/17/2023]
Abstract
We propose heat machines that are nonlinear, coherent, and closed systems composed of few field (oscillator) modes. Their thermal-state input is transformed by nonlinear Kerr interactions into nonthermal (non-Gaussian) output with controlled quantum fluctuations and the capacity to deliver work in a chosen mode. These machines can provide an output with strongly reduced phase and amplitude uncertainty that may be useful for sensing or communications in the quantum domain. They are experimentally realizable in optomechanical cavities where photonic and phononic modes are coupled by a Josephson qubit or in cold gases where interactions between photons are transformed into dipole-dipole interacting Rydberg atom polaritons. This proposed approach is a step toward the bridging of quantum and classical coherent and thermodynamic descriptions.
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Affiliation(s)
- Tomáš Opatrný
- Department of Optics, Faculty of Science, Palacký University, 17, Listopadu 50, 77146 Olomouc, Czech Republic
| | - Šimon Bräuer
- Department of Optics, Faculty of Science, Palacký University, 17, Listopadu 50, 77146 Olomouc, Czech Republic
| | - Abraham G. Kofman
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Avijit Misra
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Nilakantha Meher
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ofer Firstenberg
- Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Eilon Poem
- Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Gershon Kurizki
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
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B S R, Mukherjee V, Divakaran U. Bath Engineering Enhanced Quantum Critical Engines. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1458. [PMID: 37420478 DOI: 10.3390/e24101458] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2022] [Revised: 09/28/2022] [Accepted: 10/06/2022] [Indexed: 07/09/2023]
Abstract
Driving a quantum system across quantum critical points leads to non-adiabatic excitations in the system. This in turn may adversely affect the functioning of a quantum machine which uses a quantum critical substance as its working medium. Here we propose a bath-engineered quantum engine (BEQE), in which we use the Kibble-Zurek mechanism and critical scaling laws to formulate a protocol for enhancing the performance of finite-time quantum engines operating close to quantum phase transitions. In the case of free fermionic systems, BEQE enables finite-time engines to outperform engines operating in the presence of shortcuts to adiabaticity, and even infinite-time engines under suitable conditions, thus showing the remarkable advantages offered by this technique. Open questions remain regarding the use of BEQE based on non-integrable models.
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Affiliation(s)
- Revathy B S
- Department of Physics, Indian Institute of Technology Palakkad, Palakkad 678557, India
| | - Victor Mukherjee
- Department of Physical Sciences, IISER Berhampur, Berhampur 760010, India
| | - Uma Divakaran
- Department of Physics, Indian Institute of Technology Palakkad, Palakkad 678557, India
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Quantum engine efficiency bound beyond the second law of thermodynamics. Nat Commun 2018; 9:165. [PMID: 29323109 PMCID: PMC5765133 DOI: 10.1038/s41467-017-01991-6] [Citation(s) in RCA: 62] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2017] [Accepted: 10/31/2017] [Indexed: 11/11/2022] Open
Abstract
According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. Quantum engines operating between a thermal and a squeezed-thermal bath have been shown to surpass this bound. Yet, their maximum efficiency cannot be determined by the reversibility condition, which may yield an unachievable efficiency bound above unity. Here we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive an inequality for this change. This inequality reveals an efficiency bound for quantum engines energised by a non-thermal bath. This bound does not imply reversibility, unless the two baths are thermal. It cannot be solely deduced from the laws of thermodynamics. Evaluating maximum conversion efficiency from heat to work using non-thermal baths can lead to meaningless results, when based only on the reversibility requirement. Here, the authors solve this problem by identifying the fraction of exchanged energy that necessarily causes a change in entropy.
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Hardal AÜC, Aslan N, Wilson CM, Müstecaplıoğlu ÖE. Quantum heat engine with coupled superconducting resonators. Phys Rev E 2017; 96:062120. [PMID: 29347310 DOI: 10.1103/physreve.96.062120] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2017] [Indexed: 11/07/2022]
Abstract
We propose a quantum heat engine composed of two superconducting transmission line resonators interacting with each other via an optomechanical-like coupling. One resonator is periodically excited by a thermal pump. The incoherently driven resonator induces coherent oscillations in the other one due to the coupling. A limit cycle, indicating finite power output, emerges in the thermodynamical phase space. The system implements an all-electrical analog of a photonic piston. Instead of mechanical motion, the power output is obtained as a coherent electrical charging in our case. We explore the differences between the quantum and classical descriptions of our system by solving the quantum master equation and classical Langevin equations. Specifically, we calculate the mean number of excitations, second-order coherence, as well as the entropy, temperature, power, and mean energy to reveal the signatures of quantum behavior in the statistical and thermodynamic properties of the system. We find evidence of a quantum enhancement in the power output of the engine at low temperatures.
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Affiliation(s)
- Ali Ü C Hardal
- Department of Physics, Koç University, Sarıyer, İstanbul, 34450, Turkey.,Department of Photonics Engineering, Technical University of Denmark, Ørsteds Plads 343, DK-2800 Kgs. Lyngby, Denmark
| | - Nur Aslan
- Department of Physics, Koç University, Sarıyer, İstanbul, 34450, Turkey
| | - C M Wilson
- Institute of Quantum Computing and Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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Proesmans K, Van den Broeck C. The underdamped Brownian duet and stochastic linear irreversible thermodynamics. CHAOS (WOODBURY, N.Y.) 2017; 27:104601. [PMID: 29092424 DOI: 10.1063/1.5001187] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Building on our earlier work [Proesmans et al., Phys. Rev. X 6, 041010 (2016)], we introduce the underdamped Brownian duet as a prototype model of a dissipative system or of a work-to-work engine. Several recent advances from the theory of stochastic thermodynamics are illustrated with explicit analytic calculations and corresponding Langevin simulations. In particular, we discuss the Onsager-Casimir symmetry, the trade-off relations between power, efficiency and dissipation, and stochastic efficiency.
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