Quantum thermodynamics of Gross-Pitaevskii qubits

TL;DR

The paper develops a first-principles thermodynamic framework for nonlinear qubits, identifying a proper canonical equilibrium state for dynamics induced by a nonlinear term such as the Gross–Pitaevskii nonlinearity. It shows that nonlinear interactions raise internal energy and entropy while reducing heat capacity, and demonstrates that quantum Otto engines using nonlinear qubits achieve higher ideal and endoreversible efficiencies than their linear counterparts, with stronger gains for repulsive nonlinearity ($g<0$). The endoreversible analysis reveals that linear qubits can surpass Curzon–Ahlborn efficiency, while nonlinear qubits can outperform linear results in a nontrivial way, depending on temperature ratios. Overall, the work establishes nonlinear qubits as a new thermodynamic resource for designing more efficient quantum engines and connects nonlinear dynamics to effective many-body correlations.

Abstract

What are the resources that can be leveraged for a thermodynamic device to exhibit genuine quantum advantage? Typically, the answer to this question is sought in quantum correlations. In the present work, we show that quantum Otto engines that operate with nonlinear qubits significantly outperform linear engines. To this end, we develop a comprehensive thermodynamic description of nonlinear qubits starting with identifying the proper thermodynamic equilibrium state. We then show that for ideal cycles as well as at maximum power the efficiency of the nonlinear engine is significantly higher. Interestingly, nonlinear dynamics can be thought of as an effective description of a correlated, complex quantum many body system. Hence, our findings corroborate common wisdom, while at the same time propose a new design of more efficient quantum engines.

Figures (6)

• Figure 1: Internal energy \ref{['eq:energy_GPE']} for a Gross-Pitaevskii-type nonlinearity, $\tilde{\kappa}(z)=g z$, as a function of $g$ at $\beta=1$. Parameters are $\xi=1$, $\chi=0$, and $\zeta=2$.
• Figure 2: Internal energy \ref{['eq:energy_GPE']}, entropy \ref{['eq:entropy']}, and heat capacity with a Gross-Pitaevskii nonlinearity, $\tilde{\kappa}(z)=g z$, for $g=0$ (blue), $g=2.5$ (purple), and $g=5$ (red) as a function of temperature $T$. Parameters are $\xi=1$, $\chi=0$, and $\zeta=2$.
• Figure 3: $E-\zeta$-diagram for the ideal Otto cycle for a Gross-Pitaevskii nonlinearity, $\tilde{\kappa}(z)=gz$ for $g=0$ (blue), $g=-2.5$ (purple), and $g=-5$ (red). Parameters are $\xi=1$, $\chi=0$, $\zeta_A=1$, $\zeta_B=1.5$, $\beta_A=1$, and $\beta_D=0.5$.
• Figure 4: Efficiency of the ideal Otto cycle \ref{['eq:eta']} for qubits with a Gross-Pitaevskii nonlinearity, $\tilde{\kappa}(z)=gz$. Parameters are $\xi=1$, $\chi=0$, $\zeta_A=1$, $\zeta_B=1.5$, $\beta_A=1$, and $\beta_D=0.5$.
• Figure 5: Efficiency at maximum power of the endoreversible Otto cycle for linear qubits (red), together with the Curzon-Ahlborn efficiency \ref{['eq:CA']} (blue) and the Carnot efficiency (gray dashed). Parameters are $\xi=1$, $\chi=0$, $\alpha=1$, $\tau=1$, and $\zeta_A=1$.