[Paper Review] Supremacy of the quantum many-body Szilard engine with attractive bosons

J. Bengtsson, M. Nilsson Tengstrand+5 more|arXiv (Cornell University)|Jan 27, 2017

Advanced Thermodynamics and Statistical Mechanics28 references3 citations

TL;DR

This paper demonstrates that a quantum many-body Szilard engine using attractive bosons significantly outperforms classical and non-interacting quantum systems in work extraction. By leveraging quantum correlations from attractive interactions in a one-dimensional trap, the engine achieves a work output that exceeds the classical limit of $k_B T \ln 2$ by up to 30% at finite temperature, with performance increasing with particle number due to enhanced many-body correlations and optimized measurement outcomes.

ABSTRACT

In a classic thought experiment, Szilard suggested a heat engine where a single particle, for example an atom or a molecule, is confined in a container coupled to a single heat bath. The container can be separated into two parts by a moveable wall acting as a piston. In a single cycle of the engine, work can be extracted from the information on which side of the piston the particle resides. The work output is consistent with Landauers principle that the erasure of one bit of information costs the entropy kB ln 2, exemplifying the fundamental relation between work, heat and information. Here we apply the concept of the Szilard engine to a fully interacting quantum many-body system. We find that a working medium of a number of bosons (larger or equal two) with attractive interactions is clearly superior to other previously discussed setups. In sharp contrast to the classical case, we find that the average work output increases with the particle number. The highest overshoot occurs for a small but finite temperature, showing an intricate interplay between thermal and quantum effects. We anticipate that our finding will shed new light on the role of information in controlling thermodynamic fluctuations in the deep quantum regime, which are strongly influenced by quantum correlations in interacting systems.

Motivation & Objective

• To investigate how quantum many-body interactions influence information-to-work conversion in a Szilard engine beyond the single-particle or non-interacting regimes.
• To determine whether attractive interactions among bosons can enhance work output beyond the classical single-particle limit of $k_B T \ln 2$.
• To explore the role of quantum correlations and thermal fluctuations in optimizing work extraction in a fully interacting many-body quantum system.
• To establish a benchmark for quantum supremacy in thermodynamic cycles using exact ab initio methods for small $N \leq 5$.

Proposed method

• Exact numerical diagonalization via the full configuration interaction method to solve the many-body Schrödinger equation for up to five bosons in a one-dimensional box with a moveable barrier.
• Use of a one-dimensional model with short-range attractive interactions ($g < 0$) between bosons, parameterized by $g_0 = \hbar^2 / (L m)$.
• Implementation of a quasi-static Szilard cycle: insertion of a barrier at position $\ell^{\text{ins}}$, measurement of particle distribution, and isothermal expansion to extract work.
• Calculation of average work output as a function of temperature, interaction strength, and insertion position, using the probability distribution of measurement outcomes.
• Optimization of work output over insertion position and temperature to identify maximum performance for each system.
• Comparison of results across non-interacting bosons, repulsive bosons (Tonks-Girardeau regime), and classical particles to isolate the role of attraction and correlations.

Experimental results

Research questions

• RQ1 Can attractive interactions in a many-body quantum system lead to a work output exceeding the classical Szilard engine limit of $k_B T \ln 2$?
• RQ2 How does the work output of a quantum many-body Szilard engine scale with particle number $N$ when interactions are present?
• RQ3 What is the role of finite temperature in enhancing work output in a system with attractive bosons, given that quantum correlations and thermal fluctuations compete?
• RQ4 Why does the maximum work output occur at a finite temperature rather than at zero temperature, and what does this reveal about the interplay of quantum and thermal effects?
• RQ5 How do quantum correlations from attractive interactions modify the measurement-based work extraction process compared to non-interacting or repulsive systems?

Key findings

• The average work output for $N=4$ attractive bosons exceeds the classical limit $W_1 = k_B T \ln 2$ by up to 30% at optimal temperature and interaction strength, with the maximum occurring at finite $T \approx 0.243 \, E_1/k_B$.
• For $N=4$, the optimal work output is achieved at a symmetric barrier insertion position ($\ell^{\text{ins}} = L/2$) and attractive interaction strength $g \approx -0.01g_0$, where the probability of all particles being on one side is $p_0 \approx 0.3$, close to $1/e$.
• The relative work output $W/W_1$ increases with particle number $N$ for attractive bosons, indicating a growing quantum supremacy effect due to more favorable measurement outcomes contributing to work extraction.
• The work output for repulsive bosons converges to the non-interacting fermion limit (Tonks-Girardeau regime), where no enhancement over the classical limit is observed, confirming the uniqueness of attraction-induced supremacy.
• Non-interacting bosons show a monotonic decrease in $W/W_1$ with increasing temperature, unlike the attractive case, which exhibits a pronounced maximum at finite $T$, indicating a non-trivial interplay between thermal and quantum effects.
• Perturbative analysis suggests that the quantum supremacy effect in work output will further increase with larger $N$, despite the numerical inaccessibility of exact solutions beyond $N=5$.