Otto refrigerator based on a superconducting qubit: Classical and quantum performance

Editors' Suggestion

Otto refrigerator based on a superconducting qubit: Classical and quantum performance

B. Karimi and J. P. Pekola

Phys. Rev. B 94, 184503 – Published 9 November 2016; Erratum Phys. Rev. B 95, 019903 (2017)

Abstract

We analyze a quantum Otto refrigerator based on a superconducting qubit coupled to two $L C$ resonators, each including a resistor acting as a reservoir. We find various operation regimes: nearly adiabatic (low driving frequency), ideal Otto cycle (intermediate frequency), and nonadiabatic coherent regime (high frequency). In the nearly adiabatic regime, the cooling power is quadratic in frequency, and we find a substantially enhanced coefficient of performance $ε$ , as compared to that of an ideal Otto cycle. Quantum coherent effects lead invariably to a decrease in both cooling power and $ε$ as compared to purely classical dynamics. In the nonadiabatic regime we observe strong coherent oscillations of the cooling power as a function of frequency. We investigate various driving wave forms: Compared to the standard sinusoidal drive, a truncated trapezoidal drive with optimized rise and dwell times yields higher cooling power and efficiency.

Received 9 October 2016

DOI:https://doi.org/10.1103/PhysRevB.94.184503

Physics Subject Headings (PhySH)

Josephson effect Superconductivity Thermal properties Thermodynamics

Condensed Matter, Materials & Applied Physics

Erratum

Erratum: Otto refrigerator based on a superconducting qubit: Classical and quantum performance [Phys. Rev. B 94, 184503 (2016)]

B. Karimi and J. P. Pekola

Phys. Rev. B 95, 019903 (2017)

Authors & Affiliations

B. Karimi and J. P. Pekola

Low Temperature Laboratory, Department of Applied Physics, Aalto University School of Science, P.O. Box 13500, 00076 Aalto, Finland

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 94, Iss. 18 — 1 November 2016

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Scheme of the quantum refrigerator presented. (b) Thermodynamic Otto cycle of the refrigerator. (c) Configuration of the two-level energies of the qubit under sinusoidal driving depicted on top of the diagram.
Reuse & Permissions
Figure 2
The powers to the hot and cold reservoirs as a function of (dimensionless) frequency $Ω$ with chosen parameters ( $k_{B} T_{C} / E_{0} = k_{B} T_{H} / E_{0} = 0.3, Δ = 0.3, ω_{L C, 1} = 2 E_{0} \sqrt{\frac{1}{4} + Δ^{2}} / ℏ$ , and $ω_{L C, 2} = 2 E_{0} Δ / ℏ$ ). Different operation regimes are shown separately in the plots. (a) Quadratic dependence of the two powers on $Ω$ at low frequencies with two methods (analytical and fully numerical methods). The rising parabolas are for $Π_{1}$ and the descending ones for $Π_{2}$ . (b) Nearly ideal Otto cycle at an intermediate frequency. The solid brown line illustrates the cooling power of an ideal Otto cycle while the other three lines are numeric cooling power when $g = g_{1} = g_{2} = 1$ (solid blue line), 0.3 (dashed line), and 0.1 (dotted-dashed line). Inset of (b): The nonadiabatic regime at high frequencies associated with coherent oscillations for $Π_{1}$ (red lines) and $Π_{2}$ (black lines) with different values of $Q \equiv Q_{1} = Q_{2}$ . From top to bottom, $Q = 10$ , 30, and 100.
Reuse & Permissions
Figure 3
Dimensionless powers $Π_{i}$ as a function of $Δ$ and $g$ (inset). The blue lines show the powers for $Q = Q_{1} = Q_{2} = 10$ , red for 30, and black for 100. The green lines display powers for the ideal Otto cycle and the arrow points to the optimal value of $Δ$ in an ideal Otto cycle. The parameters are $k_{B} T_{C} / E_{0} = k_{B} T_{H} / E_{0} = 0.3, Ω = 0.01$ , and $g = g_{1} = g_{2} = 1$ , and for the inset $k_{B} T_{C} / E_{0} = k_{B} T_{H} / E_{0} = 0.3, Ω = 0.01$ , and $Δ = 0.3$ .
Reuse & Permissions
Figure 4
The variation of powers $Π_{1}$ (ascending curves) and $Π_{2}$ (descending curves) as a function of frequency in the intermediate regime. Black lines display powers for sinusoidal drive, light brown for trapezoidal drive, blue for truncated trapezoidal drive, and dark brown for ideal Otto cycle (for $Π_{2}$ ), with $g = g_{1} = g_{2} = 1$ and $Q = Q_{1} = Q_{2} = 30$ . (a) Equal temperature of the two reservoirs $(k_{B} T_{C} / E_{0} = k_{B} T_{H} / E_{0} = 0.3)$ and $Δ = 0.3$ . (b) Different bath temperatures $(k_{B} T_{H} / E_{0} = 2 k_{B} T_{C} / E_{0} = 0.3)$ and $Δ = 0.12$ . Inset in (a): The considered driving wave forms; sinusoidal, trapezoidal, and truncated trapezoidal.
Reuse & Permissions
Figure 5
Dependence of the coefficient of performance $ε$ on frequency for different drives as indicated by the names with arrows. Dotted-dashed lines correspond to ideal efficiency of the Otto refrigerator $ε_{ideal}$ , with $Q = Q_{1} = Q_{2} = 30$ and $g = g_{1} = g_{2} = 1$ for both panels. The horizontal dashed lines represent analytical results of efficiency for different drives in the low frequency regime based on Eq. (22). The parameters are (a) $k_{B} T_{H} / E_{0} = k_{B} T_{C} / E_{0} = 0.3$ and $Δ = 0.3$ , (b) $k_{B} T_{H} / E_{0} = 0.3, k_{B} T_{C} / E_{0} = 0.15$ , and $Δ = 0.12$ .
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics