Quantum Thermometry Research Articles

Exploring the role of asymmetric-pulse modulation in quantum thermal machines and quantum thermometry.

We explore the consequences of periodically modulating a quantum two-level system (TLS) with an asymmetric pulse when the system is in contact with thermal baths. By adopting the Floquet-Lindblad formalism for our analysis, we find that the unequal "up" and "down" time duration of the pulse has two main ramifications. First, the energy gap of the multiple sidebands or photon sectors created as a result of the periodic modulation are renormalized by a term which is dependent on both the modulation strength as well as the fraction of up (or down) time duration. Second, the weights of the different sidebands are no longer symmetrically distributed about the central band or zero photon sector. We illustrate the advantages of these findings in the context of applications in quantum thermal machines and thermometry. For a thermal machine constructed by coupling the TLS to two thermal baths, we demonstrate that the asymmetric pulse provides an extra degree of control over the mode of operation of the thermal machine. Further, by appropriately tuning the weight of the subbands, we also show that an asymmetric pulse may provide superior optimality in a recently proposed protocol for quantum thermometry, where dynamical control has been shown to enhance the precision of measurement.

Collective heat capacity for quantum thermometry and quantum engine enhancements

The performances of quantum thermometry in thermal equilibrium together with the output power of certain class of quantum engines share a common characteristic: both are determined by the heat capacity of the probe or working medium. After noticing that the heat capacity of spin ensembles can be significantly modified by collective coupling with a thermal bath, we build on the above observation to investigate the respective impact of such collective effect on quantum thermometry and quantum engines. We find that the precision of the temperature estimation is largely increased at high temperatures, reaching even the Heisenberg scaling—inversely proportional to the number of spins. For Otto engines operating close to the Carnot efficiency, collective coupling always enhances the output power. Some tangible experimental platforms are suggested.

Quantum thermometry based on a cavity-QED setup

We present a quantum thermometry scheme based on a cavity-QED setup, which attains a sensitivity with Heisenberg scaling. A stream of identical two-level systems passes through a thermal bath to be tested. Each system partially thermalizes, carrying information on the temperature of the thermal bath, and it then interacts with a dissipative single-mode cavity. The Heisenberg scaling is attained from the initial coherence of each system. The systems cannot be fully thermalized by the thermal bath. The optimal interaction time between the system and the thermal bath is derived. Direct photon detection is proved to be an optimal measurement when there is no extra thermal bath in the cavity. In the case where there is an extra thermal bath in the cavity independent of the thermal bath to be tested, homodyne detection is the optimal measurement. Moreover, we show that direct photon detection obtains less information in the case where the extra thermal bath in the cavity is in thermal equilibrium with the thermal bath. However, the optimal measurement can utilize the information from the extra thermal bath to improve the estimation precision of the temperature.

Two-qubit quantum probes for the temperature of an Ohmic environment

We address a particular instance where open quantum systems may be used as quantum probes for an emergent property of a complex system, as the temperature of a thermal bath. The inherent fragility of the quantum probes against decoherence is the key feature making the overall scheme very sensitive. The specific setting examined here is that of quantum thermometry, which aims to exploits decoherence as resource to estimate the temperature of a sample. We focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic regime (ranging from sub-Ohmic to super- Ohmic), by using pairs of qubits in different initial states and interacting with different environments, consisting either of a single thermal bath, or of two independent ones at the same temperature. Our scheme involves pure dephasing of the probes, thus avoiding energy exchange with the sample and the consequent perturbation of temperature itself. We discuss the interplay between correlations among the probes and correlations within the bath, and show that entanglement improves thermometry at short times whereas, if the interaction time is not constrained, coherence rather than entanglement, is the key resource in quantum thermometry.

Quantum thermometry in a squeezed thermal bath

We address the dephasing dynamics of the quantum Fisher information for the process of quantum thermometry with probes coupled to squeezed thermal baths via the nondemolition interaction. We also calculate the upper bound for the parameter estimation and investigate how the optimal estimation is affected by the initial conditions and decoherence, particularly the squeezing parameters. Moreover, the feasibility of the optimal measurement of the temperature is discussed in detail. Then, the results are generalized for entangled probes and the multi-qubit scenarios for probing the temperature are analysed. Our results show that the squeezing can decrease the number of channel uses for optimal thermometry. Comparing different schemes for multi-qubit estimation, we find that an increase in the number of the qubits, interacting with the channel, does not necessarily vary the precision of estimating the temperature. Besides, we discuss the enhancement of the quantum thermometry using the parallel strategy and starting from the W state.

Enhanced precision bound of low-temperature quantum thermometry via dynamical control

High-precision low-temperature thermometry is a challenge for experimental quantum physics and quantum sensing. Here we consider a thermometer modeled by a dynamically-controlled multilevel quantum probe in contact with a bath. Dynamical control in the form of periodic modulation of the energy-level spacings of the quantum probe can dramatically increase the maximum accuracy bound of low-temperatures estimation, by maximizing the relevant quantum Fisher information. As opposed to the diverging relative error bound at low temperatures in conventional quantum thermometry, periodic modulation of the probe allows for low-temperature thermometry with temperature-independent relative error bound. The proposed approach may find diverse applications related to precise probing of the temperature of many-body quantum systems in condensed matter and ultracold gases, as well as in different branches of quantum metrology beyond thermometry, for example in precise probing of different Hamiltonian parameters in many-body quantum critical systems.

Temperature quantum sensor on superradiant phase-transition

We study superradiant phase-transition (SPT) phenomena for high-precision quantum thermometry applications. Comprehensive thermodynamic properties of quantum thermosensor have been elucidated. Such thermosensor exploits two distinguishable thermodynamic (collective) states of N inhomogeneously broadened two-level quantum systems (TLSs) interacting with a quantized electromagnetic field in the cavity. Field amplitude (cavity photon number) represents the order parameter and exhibits the second order phase-transition. We fully describe two types of exciton-polaritons being close to normal state, which can be used for initialization of operating regimes in temperature sensorics. Temperature sensitivity and accuracy are analyzed in the framework of quantum estimation theory. Scaling for standard quantum limit (SQL), up to Heisenberg limit for temperature estimation, has been predicted. Temperature accuracy estimation up to mK’s and beyond can be achieved with use of phase-transition with a lower branch exciton-polaritons. It can be obtained with currently available narrow band semiconductor microstructures placed in microcavities with high Q-factor.

Collisional Quantum Thermometry.

We introduce a general framework for thermometry based on collisional models, where ancillas probe the temperature of the environment through an intermediary system. This allows for the generation of correlated ancillas even if they are initially independent. Using tools from parameter estimation theory, we show through a minimal qubit model that individual ancillas can already outperform the thermal Cramer-Rao bound. In addition, due to the steady-state nature of our model, when measured collectively the ancillas always exhibit superlinear scalings of the Fisher information. This means that even collective measurements on pairs of ancillas will already lead to an advantage. As we find in our qubit model, such a feature may be particularly valuable for weak system-ancilla interactions. Our approach sets forth the notion of metrology in a sequential interactions setting, and may inspire further advances in quantum thermometry.

Fundamental limits on low-temperature quantum thermometry with finite resolution

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 tight-binding 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 square-lattice Ising model, highlighting the role of phase transitions.

A CMOS-integrated quantum sensor based on nitrogen–vacancy centres

The nitrogen vacancy (NV) center in diamond has emerged as a leading solid-state quantum sensor for applications including magnetometry, electrometry, thermometry, and chemical sensing. However, an outstanding challenge for practical applications is that existing NV-based sensing techniques require bulky and discrete instruments for spin control and detection. Here, we address this challenge by integrating NV based quantum sensing with complementary metal-oxide-semiconductor (CMOS) technology. Through tailored CMOS-integrated microwave generation and photodetection, this work dramatically reduces the instrumentation footprint for quantum magnetometry and thermometry. This hybrid diamond-CMOS integration enables an ultra-compact and scalable platform for quantum sensing and quantum information processing.

Dynamical role of quantum signatures in quantum thermometry

Classifying quantum states usually demands to observe properties such as the amount of correlation at one point in time. Further insight may be gained by inspecting the dynamics in a given evolution scheme. Here we attempt such a classification looking at single-qubit and two-qubit states at the start of thermalisation with a heat bath. The speed with which the evolution starts is influenced by quantum aspects of the state, however, such signatures do not allow for a systematic classification.

Quantum thermometry by single-qubit dephasing

We address the dephasing dynamics of a qubit as an effective process to estimate the temperature of its environment. Our scheme is inherently quantum, since it exploits the sensitivity of the qubit to decoherence, and does not require thermalization with the system under investigation. We optimize the quantum Fisher information with respect to the interaction time and the temperature in the case of Ohmic-like environments. We also find explicitly the qubit measurement achieving the quantum Cramer- Rao bound to precision. Our results show that the conditions for optimal estimation originate from a non-trivial interplay between the dephasing dynamics and the Ohmic structure of the environment. In general, optimal estimation is achieved neither when the qubit approaches the stationary state, nor for full dephasing.

Fiber-Optic Quantum Thermometry with Germanium-Vacancy Centers in Diamond

Accurate, high spatial resolution thermal measurements have provided fundamental insights into many fields of study; however, existing thermometer technology often suffers from one or more limitati...

Calibrated quantum thermometry in cavity optomechanics

Cavity optomechanics has achieved the major breakthrough of the preparation and observation of macroscopic mechanical oscillators in non-classical states. The development of reliable indicators of the oscillator properties in these conditions is important also for applications to quantum technologies. We compare two procedures to infer the oscillator occupation number, minimizing the necessity of system calibrations. The former starts from homodyne spectra, the latter is based on the measurement of the motional sideband asymmetry in heterodyne spectra. Moreover, we describe and discuss a method to control the cavity detuning, that is a crucial parameter for the accuracy of the latter, intrinsically superior procedure.

Using Polarons for sub-nK Quantum Nondemolition Thermometry in a Bose-Einstein Condensate.

We introduce a novel minimally disturbing method for sub-nK thermometry in a Bose-Einstein condensate (BEC). Our technique is based on the Bose polaron model; namely, an impurity embedded in the BEC acts as the thermometer. We propose to detect temperature fluctuations from measurements of the position and momentum of the impurity. Crucially, these cause minimal backaction on the BEC and hence, realize a nondemolition temperature measurement. Following the paradigm of the emerging field of quantum thermometry, we combine tools from quantum parameter estimation and the theory of open quantum systems to solve the problem in full generality. We thus avoid any simplification, such as demanding thermalization of the impurity atoms, or imposing weak dissipative interactions with the BEC. Our method is illustrated with realistic experimental parameters common in many labs, thus showing that it can compete with state-of-the-art destructive techniques, even when the estimates are built from the outcomes of accessible (suboptimal) quadrature measurements.

Quantum thermometry with trapped ions

We introduce the estimation protocol for detecting the temperature of the transverse vibrational modes of linear ion crystal. We show that thanks to the laser induced laser coupling between the vibrational modes and the collective spin states the estimation of the temperature is carried out by set of measurements of the spin populations. We show that temperature estimation protocol using single ion as a quantum probe is optimal in a sense that the set of state projective measurement saturates the fundamental Cramer-Rao bound. We find a plateau of the maximal temperature sensitivity using ion chain as a quantum probe. Moreover, we show that the non-classical part of the quantum Fisher information could leads to enhancement of the temperature sensitivity compared to the single ion case.

Bridging thermodynamics and metrology in nonequilibrium quantum thermometry

Single-qubit thermometry presents the simplest tool to measure the temperature of thermal baths with reduced invasivity. At thermal equilibrium, the temperature uncertainty is linked to the heat capacity of the qubit, however the best precision is achieved outside equilibrium condition. Here, we discuss a way to generalize this relation in a non-equilibrium regime, taking into account purely quantum effects such as coherence. We support our findings with an experimental photonic simulation.

Dynamical approach to ancilla-assisted quantum thermometry

A scheme for improving the sensitivity of quantum thermometry is proposed where the sensing quantum system used to recover the temperature of an external bath is dynamically coupled with an external ancilla (a meter) via a Hamiltonian term $\hat{H}_I$. At variance with previous approaches, our scheme relies neither on the presence of initial entanglement between the sensor and the meter, nor on the possibility of performing joint measurements on the two systems. The advantages we report arise from the fact that the presence of $\hat{H}_I$ interferes with the bath-sensor interaction, transforming the sensor into an effective transducer which extracts the intrinsically incoherent information on the bath temperature, and maps it into coherences in the meter where it can finally be recovered by local measurements.

Growth of polycrystalline and single-crystal CVD diamonds with bright photoluminescence of Ge-V color centers using germane GeH4 as the dopant source

Germanium-Vacancy (Ge-V) color center in diamond possesses a narrow band photoluminescence (PL) emission in the orange spectral range interesting as a single-photon source for quantum optical technologies and thermometry, therefore, development of methods for the controllable doping of diamond with Ge is of high importance for such applications. Here, we report on the synthesis of polycrystalline and epitaxial single crystal Ge-doped films using microwave plasma chemical vapor deposition (CVD) technique by addition of the germane GeH4 gas into the H2-CH4 plasma. It is demonstrated, that GeH4 addition affects the CVD growth of microcrystalline diamond, reducing the film growth rate and increasing the average diamond grain size. The films show bright photoluminescence of Ge-V centers at ≈602 nm under the optimized GeH4 concentration, with a zero-phonon line width of 1.6 nm (FWHM) for Ge-V ensemble at low temperatures (5 K). The developed in-situ doping from the germane gas opens a way for a better control of the Ge-V color center formation in diamond for photonic applications.

All-optical quantum thermometry based on spin-level cross-relaxation and multicenter entanglement under ambient conditions in SiC

All-optical thermometry technique based on the energy level cross-relaxation in atomic-scale spin centers in SiC is demonstrated. This technique exploits a giant thermal shift of the zero-field splitting for centers in the triplet ground state, S=1, undetected by photoluminescence (so called “dark” centers) coupling to neighbouring spin-3/2 centers which can be optically polarized and read out (“bright” centers), and does not require radiofrequency fields. EPR was used to identify defects. The width of the cross-relaxation line is almost an order of magnitude smaller than the width of the excited state level-anticrossing line, which was used in all-optical thermometry and which can not be significantly reduced since determined by the lifetime of the excited state. With approximately the same temperature shift and the same signal intensities as for excited state level-anticrossing, cross-relaxation signal makes it possible to increase the sensitivity of the temperature measurement by more than an order of magnitude. Temperature sensitivity is estimated to be approximately 10 mK/Hz1/2 within a volume about 1 μ3, allocated by focused laser excitation in a scanning confocal microscope. Using cross-relaxation in the ground states of “bright” spin-3/2 centers and “dark” S=1 centers for temperature sensing and ground state level anti-crossing of “bright” spin-3/2 centers an integrated magnetic field and temperature sensor with submicron space resolution can be implemented using the same spin system. The coupling of individually addressable “bright” spin-3/2 centers connected by a chain of “dark” S=1 spins, could be considered in quantum information processing and multicenter entanglement under ambient conditions.