Universal locality of quantum thermal susceptibility

Palma, Giacomo De; Pasquale, Antonella De; Giovannetti, Vittorio

doi:10.1103/physreva.95.052115

Cited by 30 publications

(30 citation statements)

References 68 publications

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“…The exponentially diverging error is a consequence of the fact that for temperatures far below the lowest gap, the system is essentially in the ground state, irrespective of the exact value of T . Such an exponentially diverging error was found in various studies on low-temperature thermometry (see, e.g., [6][7][8][9][10][11][12][13][14][15][16][17][19][20][21][22]). In particular, Eq.…”

Section: Context and Main Resultsmentioning

confidence: 53%

“…ponentially at low temperatures [6][7][8][9][10][11][12][13][14][15][16][17]. In fact, this exponential scaling can be derived from very general arguments [18][19][20][21], based on the energy spectra of the sample and the probe, and could therefore appear to represent a fundamental limit on thermometry. However, it was recently shown that (using a measurement with infinite resolution) a sub-exponential scaling is possible in a system of strongly coupled harmonic oscillators [22].…”

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confidence: 99%

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Fundamental limits on low-temperature quantum thermometry with finite resolution

Potts

Brask

Brunner

2019

Quantum

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While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we develop a general approach to low-temperature quantum thermometry, taking into account restrictions arising not only from the sample but also from the measurement process. We derive a fundamental bound on the minimal uncertainty for any temperature measurement that has a finite resolution. A similar bound can be obtained from the third law of thermodynamics. Moreover, we identify a mechanism enabling sub-exponential scaling, even in the regime of finite resolution. We illustrate this effect in the case of thermometry on a fermionic tightbinding chain with access to only two lattice sites, where we find a quadratic divergence of the uncertainty. We also give illustrative examples of ideal quantum gases and a squarelattice Ising model, highlighting the role of phase transitions.

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Section: Context and Main Resultsmentioning

confidence: 53%

mentioning

confidence: 99%

Fundamental limits on low-temperature quantum thermometry with finite resolution

Potts

Brask

Brunner

2019

Quantum

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“…More generally, any measurement on the sample, implemented using a finite-sized apparatus, comes with a lower bound on the attainable resolution of, e.g., the system energy spectrum [30][31][32]. Similar restrictions apply in situations where measurements can be made on only part of a large sample [33][34][35], and clearly such finite-resolution constraints must play an important role in formulating fundamental bounds on the attainable thermometric sensitivity.…”

Section: Introductionmentioning

confidence: 99%

Tight bound on finite-resolution quantum thermometry at low temperatures

Jørgensen

Potts

Paris

et al. 2020

Phys. Rev. Research

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Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero. The bound demonstrates that under finite resolution, the variance in any temperature estimate must decrease slower than linearly. This scaling can be saturated by monitoring the nonequilibrium dynamics of a single-qubit probe. We support this finding by numerical simulations of a spin-boson model. In particular, this shows that thermometry with a vanishing absolute error at low temperature is possible with finite resolution, answering an interesting question left open by previous work. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantum thermometry, and practically, in guiding the development of sensitive thermometric techniques applicable at ultracold temperatures.

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“…Although thermometrically useful non-demolition global measurements can sometimes be implemented [6,[17][18][19], these schemes rely on measurements of additive quantities and thus cannot be optimal for strongly interacting systems. This motivates the development of minimally invasive "local" thermometric strategies, aimed at inferring the global temperature from measurements on an accessible small fraction of the system [7,20].…”

Section: Introductionmentioning

confidence: 99%

Measuring the temperature of cold many-body quantum systems

2018

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Precise low-temperature thermometry is a key requirement for virtually any quantum technological application. Unfortunately, as the temperature T decreases, the errors in its estimation diverge very quickly. In this paper, we determine exactly how quickly this may be. We rigorously prove that the "conventional wisdom" of low-T thermometry being exponentially inefficient, is limited to local thermometry on translationally invariant systems with short-range interactions, featuring a non-zero gap above the ground state. This result applies very generally to spin and harmonic lattices. On the other hand, we show that a power-law-like scaling is the hallmark of local thermometry on gapless systems. Focusing on thermometry on one node of a harmonic lattice, we obtain valuable physical insight into the switching between the two types of scaling. In particular, we map the problem to an equivalent setup, consisting of a Brownian thermometer coupled to an equilibrium reservoir. This mapping allows us to prove that, surprisingly, the relative error of local thermometry on gapless harmonic lattices does not diverge as T → 0; rather, it saturates to a constant. As a useful by-product, we prove that the low-T sensitivity of a harmonic probe arbitrarily strongly coupled to a bosonic reservoir by means of a generic Ohmic interaction, always scales as T 2 for T → 0. Our results thus identify the energy gap between the ground and first excited states of the global system as the key parameter in local thermometry, and ultimately provide clues to devising practical thermometric strategies deep in the ultra-cold regime.

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Universal locality of quantum thermal susceptibility

Cited by 30 publications

References 68 publications

Fundamental limits on low-temperature quantum thermometry with finite resolution

Fundamental limits on low-temperature quantum thermometry with finite resolution

Tight bound on finite-resolution quantum thermometry at low temperatures

Measuring the temperature of cold many-body quantum systems

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