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arXiv:2205.11997 · Advanced Quantum Technologies

Optimal Temperature Estimation in Polariton Bose‐Einstein Condensate

Dong Xie, Chunling Xu

Published Oct 13, 2022• 1 citation
arXivHTMLPDF

Abstract

Abstract Improving the measurement precision of temperature is very important and challenging, especially at low temperatures. Based on the existence of invariant subspaces during the polariton thermalization, a new way to enhance the measurement precision of low temperature is proposed and the Landau bound is obtained to avoid that the measurement uncertainty of the temperature diverges as the temperature approaches zero. The measurement precision of low temperature increases significantly with the number of polariton states. In order to resist the dissipation, the incoherent pumping is necessary for obtaining the information of the temperature encoded in the steady state. It should be noted that too strong incoherent pumping is wasteful due to that the quantum Fisher information of the temperature becomes less and less dependent on the total number of the polaritons.

DOI
10.1002/qute.202200085

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Abstract Improving the measurement precision of temperature is very important and challenging, especially at low temperatures. Based on the existence of invariant subspaces during the polariton thermalization, a new way to enhance the measurement precision of low temperature is proposed and the Landau bound is obtained to avoid that the measurement uncertainty of the temperature diverges as the temperature approaches zero. The measurement precision of low temperature increases significantly with the number of polariton states. In order to resist the dissipation, the incoherent pumping is necessary for obtaining the information of the temperature encoded in the steady state. It should be noted that too strong incoherent pumping is wasteful due to that the quantum Fisher information of the temperature becomes less and less dependent on the total number of the polaritons.
Improving the measurement precision of low temperature is significant in fundamental science and advanced quantum technology application. However, the measurement precision of temperature T usually diverges as T tends to zero. Here, by utilizing a heavy impurity to measure the temperature of a Bose gas, we obtain the Landau bound to precision δ 2 T ∝ T 2 to avoid the divergence. When the initial momentum of the heavy impurity is close to be fixed and nonzero, the measurement precision can be δ 2 T ∝ T 3 to break the Landau bound. We derive the momentum distribution of the heavy impurity at any moment and obtain the optimal measurement precision of the temperature by calculating the Fisher information. As a result, we find that increasing the expectation value P 0 and reducing the variance Δ / 2 of the initial momentum can help to improve the measurement precision. Moreover, under certain conditions, Δ / P 0 is a relevant parameter, the smallness of which helps improve the thermometric precision of the probe. In addition, the momentum measurement is the optimal measurement of the temperature in the case that the initial momentum is close to be fixed and not equal to zero. The kinetic energy measurement is the optimal measurement in the case that the expectation value of the initial momentum is close to zero. Finally, we obtain that the temperatures of two Bose gases can be measured simultaneously. The simultaneous measurement precision is proportional to T 2 when two temperatures are close to T . Published by the American Physical Society 2024
We study the role of bath-induced correlations in temperature estimation of cold bosonic baths. Our protocol includes multiple probes, that are not interacting, nor are they initially correlated to each other. They interact with a bosonic sample and reach a nonthermal steady state, which is measured to estimate the temperature of the sample. It is well known that in the steady state such noninteracting probes may get correlated to each other and even entangled. Nonetheless, the impact of these correlations in metrology has not been deeply investigated yet. Here, we examine their role for thermometry of cold bosonic gases and show that, although being classical, bath-induced correlations can lead to significant enhancement of precision for thermometry. The improvement is especially important at low temperatures, where attaining high precision thermometry is particularly demanding. The proposed thermometry scheme does not require any precise dynamical control of the probes and tuning the parameters and is robust to noise in initial preparation, as it is built upon the steady state generated by the natural dissipative dynamics of the system. Therefore, our results put forward new possibilities in thermometry at low temperatures, of relevance, for instance, in cold gases and Bose-Einstein condensates.
The precise measurement of low temperatures is significant for both the fundamental understanding of physical processes and technological applications. In this work, we present a method for low-temperature measurement that improves thermal range and sensitivity by generating quantum coherence in a thermometer probe. Typically, in temperature measurements, the probes thermalize with the sample being measured. However, we use a two-level quantum system, or qubit, as our probe and prevent direct probe access to the sample by introducing a set of ancilla qubits as an interface. We describe the open system dynamics of the probe using a global master equation and demonstrate that while the ancilla-probe system thermalizes with the sample, the probe per se evolves into a nonthermal steady state due to nonlocal dissipation channels. The populations and coherences of this steady state depend on the sample temperature, allowing for precise and wide-range low-temperature estimation. We characterize the thermometric performance of the method using quantum Fisher information and show that the quantum Fisher information can exhibit multiple and higher peaks at different low temperatures with increasing quantum coherence and the number of ancilla qubits. Our analysis reveals that the proposed approach, using a nonthermal qubit thermometer probe with temperature-dependent quantum coherence generated by a multiple qubit interface between a thermal sample and the probe qubit, can enhance the sensitivity of temperature estimation and broaden the measurable low-temperature range.
Abstract Quantum thermometry refers to the study of measuring ultra-low temperatures in quantum systems. The precision of such a quantum thermometer is limited by the degree to which temperature can be estimated by quantum measurements. More precisely, the maximal precision is given by the inverse of the quantum Fisher information. In the present analysis, we show that quantum thermometers that are described by nonlinear Schrödinger equations allow for a significantly enhanced precision, that means larger quantum Fisher information. This is demonstrated for a variety of pedagogical scenarios consisting of single and two-qubits systems. The enhancement in precision is indicated by non-vanishing quantum speed limits, which originate in the fact that the thermal, Gibbs state is typically not invariant under the nonlinear equations of motion.
The rapidly developing quantum technologies and thermodynamics have put forward a requirement to precisely control and measure the temperature of microscopic matter at the quantum level. Many quantum thermometry schemes have been proposed. However, precisely measuring low temperature is still challenging because the obtained sensing errors generally tend to diverge with decreasing temperature. Using a continuous-variable system as a thermometer, we propose non-Markovian quantum thermometry to measure the temperature of a quantum reservoir. A mechanism to make the sensing error $\ensuremath{\delta}T$ scale with the temperature TTT as the Landau bound $\ensuremath{\delta}T\ensuremath{\simeq}T$ in the full-temperature regime is discovered. Our analysis reveals that it is the quantum criticality of the total thermometer-reservoir system that causes this enhanced sensitivity. Efficiently avoiding the error-divergence problem, our result gives an efficient way to precisely measure the low temperature of quantum systems.
We propose a theoretical scheme for quantum sensing of temperature close to absolute zero in a quasi-one-dimensional Bose-Einstein condensate (BEC). In our scheme, a single-atom impurity qubit is used as a temperature sensor. We investigate the sensitivity of the single-atom sensor in estimating the temperature of the BEC. We demonstrate that the sensitivity of the temperature sensor can saturate the quantum Cram\'er-Rao bound by means of measuring quantum coherence of the probe qubit. We study the temperature sensing performance by using quantum signal-to-noise ratio (QSNR). It is indicated that there is an optimal encoding time at which the QSNR can reach its maximum in the full-temperature regime. In particular, we find that the QSNR reaches a finite upper bound in the weak coupling regime even when the temperature is close to absolute zero, which implies that the sensing-error-divergence problem is avoided in our scheme. Our work opens a way for quantum sensing of temperature close to absolute zero in the BEC.