Theory of quantum-circuit refrigeration by photon-assisted electron tunneling

Silveri, Matti; Grabert, Hermann; Masuda, S.; Tan, Kuan Yen; Möttönen, Mikko

doi:10.1103/physrevb.96.094524

Cited by 45 publications

(129 citation statements)

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“…Furthermore, the role of dissipation in phase transitions of open many-body quantum systems has attracted great interest through the recent progress in studying synthetic quantum matter 16,17 .In our experimental setup, the system exhibiting the Lamb shift is a superconducting coplanar waveguide resonator with the resonance frequency ω r /2π = 4.7 GHz and 8.5 GHz for Sample A and B, respectively, with loaded quality factors in the range of 10 2 to 10 3 . The total Lamb shift includes two parts: the dynamic part 2,27,28 arising from the fluctuations of the broadband electromagnetic environment formed by electron tunneling across normal-metal-insulator-superconductor junctions 14,15,19,29 (Fig. 1) and the static shift originating here from the environment-induced change of the resonator mode.…”

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Broadband Lamb shift in an engineered quantum system

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The shift of energy levels owing to broadband electromagnetic vacuum fluctuations-the Lamb shift-has been pivotal in the development of quantum electrodynamics and in understanding atomic spectra 1-6 . Currently, small energy shifts in engineered quantum systems are of paramount importance owing to the extreme precision requirements in applications such as quantum computing 7,8 . However, without a tunable environment it is challenging to resolve the Lamb shift in its original broadband case. Consequently, the observations in other than atomic systems [1][2][3][4][5]9 are limited to environments comprised of narrowband modes 10-12 . Here, we observe a broadband Lamb shift in high-quality superconducting resonators, a scenario also accessing any static shift inaccessible in Lamb's experiment 1,2 . We measure a continuous change of several megahertz in the fundamental resonator frequency by externally tuning the coupling strength of the engineered broadband environment which is based on hybrid normal-metal-superconductor tunnel junctions [13][14][15] . Our results may lead to improved control of dissipation in high-quality engineered quantum systems and open new possibilities for studying synthetic open quantum matter 16-18 using this hybrid experimental platform.Physical quantum systems are always open. Thus, exchange of energy and information with an environment eventually leads to relaxation and degradation of quantum coherence. Interestingly, the environment can be in a vacuum state and yet cause significant perturbation to the original quantum system. The quantum vacuum can be modelled as broadband fluctuations which may absorb energy from the coupled quantum systems. These fluctuations also lead to an energy level renormalizationthe Lamb shift-of the system, such as that observed in atomic systems [1][2][3][4][5]9 . Despite of its fundamental nature, the Lamb shift arising from broadband fluctuations is often overlooked outside the field of atomic physics as a small constant shift that is challenging to distinguish 20 . Due to the emergence of modern engineered quantum systems, in which the desired precision of the energy levels is comparable to the Lamb shift, it has, however, become important to predict accurately the perturbation as a function of external control parameters. Neglecting energy shifts can potentially take the engineered quantum systems outside the region of efficient operation 21,22 and may even lead to undesired level crossings between subsystems. These issues are pronounced in applications requiring strong dissipation. Examples include reservoir engineering for autonomous quantum error correction 23,24 , or rapid on-demand entropy and heat evacuation 14,15,25,26 . Furthermore, the role of dissipation in phase transitions of open many-body quantum systems has attracted great interest through the recent progress in studying synthetic quantum matter 16,17 .In our experimental setup, the system exhibiting the Lamb shift is a superconducting coplanar waveguide resonator with the resonance frequ...

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“…The red arrow corresponds to photon emission. Elastic processes (black arrow) do not affect the resonator state but contribute to the Lamb shift and to the thermalization of the normal-metal island 19 . The bias voltage V shifts the electrochemical potentials of the normal metal and of the superconductor relative to each other by eV .…”

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Broadband Lamb shift in an engineered quantum system

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“…The case (i) is met in an experiment where the qubit is initialized using a heat sink to a heat bath at the same temperature as the electromagnetic environment of the resonator. In case (ii), we assume that the electron temperature of the QCR equals that of the resonator environment, and since the QCR can cool to half of its electron temperature [20], we t that are numerically simulated according to master equation (8). The markers of different colors correspond to different initial deviations δ 0 as indicated.…”

Section: Resonator Initialization By Stabilizationmentioning

confidence: 99%

“…In this work, we tackle the trade-off problem by utilizing tunable electromagnetic environments such as the recently demonstrated quantum-circuit refrigerator [19,20] (QCR). Coupled to a quantum device such as a resonator or a qubit, the QCR allows fast and flexible control over the relaxation rate of the coupled element.…”

Section: Introductionmentioning

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Accelerated stabilization of coherent photon states

Ikonen

Möttönen

2018

New J. Phys.

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Control and utilization of coherent states of microwave photons is a ubiquitous requirement for the present and near-future implementations of solid-state quantum computers. The rate at which the photon state responds to external driving is limited by the relaxation rate of the storage resonator, which poses a trade-off between fast control and long storage time. Here, we present a control scheme that is designed to drive an unknown photon state to a desired coherent state much faster than the resonator decay rate. Our method utilizes a tunable environment which acts on an ancillary qubit coupled to the resonator. By periodically resetting the qubit and tuning it into resonance with the resonator, possible photon loss and dephasing of the resonator mode are corrected without measurements or active feedback. In general, our method is suitable for accelerating the control of coherent states in high-fidelity resonators.

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“…Mesoscopic refrigerators based on this effect make use of semiconductor quantum dots 7,8 , superconducting-insulator-normal metal (SIN) junctions [9][10][11][12] , or single-electron transistors (SET) 13,14 . Cooling mediated by the coupling to cavity photons has also been proposed in Josephson junctions [15][16][17] and implemented for the refrigeration of metallic islands [18][19][20][21][22] . Here an alternative approach is proposed based on the capacitive coupling of a two-terminal SINIS SET to the system to be cooled, see Fig.…”

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Correlation-induced refrigeration with superconducting single-electron transistors

Sánchez

2017

Applied Physics Letters

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A model of a superconducting tunnel junction which refrigerates a nearby metallic island without any particle exchange is presented. Heat extraction is mediated by charge fluctuations in the coupling capacitance of the two systems. The interplay of Coulomb interaction and the superconducting gap reduces the power consumption of the refrigerator. The island is predicted to be cooled from lattice temperatures of 200 mK down to close to 50 mK, for realistic parameters. The results emphasize the role of non-equilibrium correlations in bipartite mesoscopic conductors. This mechanism can be applied to create local temperature gradients in tunnel junction arrays or explore the role of interactions in the thermalization of non-equilibrium systems.Quantum coherent processes relevant to quantum information or quantum thermodynamics 1 are usually damaged by temperature. Solid state quantum simulators 2 or heat engines 3,4 have recently been proposed that operate at very low temperatures. Finding ways to cool nanoscale systems 5,6 , or introduce local temperature gradients well below 100 mK without injecting charge into them is hence a demanding task. This way they are minimally perturbed and not affected by Joule heating.Thermoelectric refrigeration is traditionally based on the Peltier effect. Driving a current through a conductor with broken electron-hole symmetry converts thermal excitations into transport. Mesoscopic refrigerators based on this effect make use of semiconductor quantum dots 7,8 , superconducting-insulator-normal metal (SIN) junctions 9-12 , or single-electron transistors (SET) 13,14 . Cooling mediated by the coupling to cavity photons has also been proposed in Josephson junctions 15-17 and implemented for the refrigeration of metallic islands [18][19][20][21][22] . Here an alternative approach is proposed based on the capacitive coupling of a two-terminal SINIS SET to the system to be cooled, see Fig. 1. We consider cooling of a single-electron box (SEB) 23,24 : a Coulomb blockade island which exchanges electrons with a third terminal. The extraction of energy is mediated by the Coulomb repulsion of electrons in different islands, J. The superconducting gap, ∆, acts as an energy filter: At subgap voltages, only transitions that take energy from from the capacitor contribute to transport. A normal metal SET would unavoidably emit Joule heat at all voltages into the island. The manipulation of electrical and thermal flows in capacitively coupled normal metal or semiconductor systems has been recently demonstrated, including effects such as quantum dot heat engines 25-32 , autonomous Maxwell's demon operations 33,34 , thermal rectifiers 35-37 , memristors 38 , or single-electron current switches 39-41 . The interplay of the two relevant energy scales, J and ∆, in the cooling mechanism is investigated. Subgap transport in the SET is assisted by the Coulomb interaction, hence increasing the voltage window where cooling takes place. Hot electrons in the SET island are thus pumped over the gap of the supercond...

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Theory of quantum-circuit refrigeration by photon-assisted electron tunneling

Cited by 45 publications

References 58 publications

Broadband Lamb shift in an engineered quantum system

Broadband Lamb shift in an engineered quantum system

Accelerated stabilization of coherent photon states

Correlation-induced refrigeration with superconducting single-electron transistors

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