We address estimation of temperature for a micromechanical oscillator lying arbitrarily close to its quantum ground state. Motivated by recent experiments, we assume that the oscillator is coupled to a probe qubit via Jaynes-Cummings interaction and that the estimation of its effective temperature is achieved via quantum-limited measurements on the qubit. We first consider the ideal unitary evolution in a noiseless environment and then take into account the noise due to nondissipative decoherence. We exploit local quantum estimation theory to assess and optimize the precision of estimation procedures based on the measurement of qubit population and to compare their performances with the ultimate limit posed by quantum mechanics. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over the possible qubit preparations and interaction times, and compare its behavior with that of the quantum Fisher information (QFI). We found that the FI for population measurement is equal to the QFI, i.e., population measurement is optimal, for a suitable initial preparation of the qubit and a predictable interaction time. The same configuration also corresponds to the maximum of the QFI itself. Our results indicate that the achievement of the ultimate bound to precision allowed by quantum mechanics is in the capabilities of the current technology.

By making use of a recently proposed framework for the inference of thermodynamic irreversibility in bosonic quantum systems, we experimentally measure and characterize the entropy production rates in the nonequilibrium steady state of two different physical systems -a micro-mechanical resonator and a Bose-Einstein condensate -each coupled to a high finesse cavity and hence also subject to optical loss. Key features of our setups, such as cooling of the mechanical resonator and signatures of a structural quantum phase transition in the condensate are reflected in the entropy production rates. Our work demonstrates the possibility to explore irreversibility in driven mesoscopic quantum systems and paves the way to a systematic experimental assessment of entropy production beyond the microscopic limit.Entropy is a crucial quantity for the characterisation of dynamical processes: it quantifies and links seemingly distant notions such as disorder, information, and irreversibility across different disciplinary boundaries [1,2]. Every finitetime transformation results in some production of entropy, which signals the occurrence of irreversibility. Quantifying the amount of irreversible entropy produced by a given process is a goal of paramount importance: entropy production is a key quantity for the characterisation of non-equilibrium processes, and its minimisation improves the efficiency of thermal machines. The second law of thermodynamics can be formulated in terms of a universal constraint on the entropy production, which can never be negative [3,4]. In turn, this leads to the following rate equation for the variation of the entropy S [5]where Π(t) and Φ(t) are the irreversible entropy production rate and the entropy flux from the system to the environment, respectively. When the system reaches a non-equilibrium steady-state (NESS) these quantities take values Π s and Φ s respectively, such that Π s = Φ s > 0 [see Fig. 1 (a)]. Under these conditions, entropy is produced and exchanged with the local baths at the same rate. Only when both terms vanish (Π s = Φ s = 0) one recovers thermal equilibrium. The entropy production rate directly accounts for the irreversibility of a process and uncovers the non-equilibrium features of a system. The link between the entropy production rate Π s and irreversibility becomes particularly relevant in small systems subjected to fluctuations, for which a microscopic definition of entropy production based on stochastic trajectories of the system has been given [6]. Experimentally, this notion has been used to test fluctuation theorems in a variety of classically operating systems such as a single-electron box [7], a two-level system driven by a time-dependent potential [8], and a levitated nanoparticle undergoing relaxation [9]. However, in order to harness the working principles of thermodynamic machines working at the quantum level, and pinpoint the differences between their performances and those of their classical counterparts, it is important to analyse the entropy generated thro...

Directional amplification, in which signals are selectively amplified depending on their propagation direction, has attracted much attention as key resource for applications, including quantum information processing. Recently, several, physically very different, directional amplifiers have been proposed and realized in the lab. In this work, we present a unifying framework based on topology to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays. Specifically, we unveil a one-to-one correspondence between a non-zero topological invariant defined on the spectrum of the dynamic matrix and regimes of directional amplification, in which the end-to-end gain grows exponentially with the number of cavities. We compute analytically the scattering matrix, the gain and reverse gain, showing their explicit dependence on the value of the topological invariant. Parameter regimes achieving directional amplification can be elegantly obtained from a topological ‘phase diagram’, which provides a guiding principle for the design of both phase-preserving and phase-sensitive multimode directional amplifiers.

We use the theory of quantum estimation in two different qubit-boson coupling models to demonstrate that the temperature of a quantum harmonic oscillator can be estimated with high precision by quantum-limited measurements on the qubit. The two models that we address embody situations of current physical interest due to their connection with ongoing experimental efforts on the control of mesoscopic dynamics. We show that population measurements performed over the qubit probe are near optimal for a broad range of temperatures of the harmonic oscillator.

We address the out-of-equilibrium thermodynamics of an isolated quantum system consisting of a cavity optomechanical device. We explore the dynamical response of the system when driven out of equilibrium by a sudden quench of the coupling parameter and compute analytically the full distribution of the work generated by the process. We consider linear and quadratic optomechanical coupling, where the cavity field is parametrically coupled to either the position or the square of the position of a mechanical oscillator, respectively. In the former case we find that the average work generated by the quench is zero, whilst the latter leads to a non-zero average value. Through fluctuations theorems we access the most relevant thermodynamical figures of merit, such as the free energy difference and the amount of irreversible work generated. We thus provide a full characterization of the out-of-equilibrium thermodynamics in the quantum regime for nonlinearly coupled bosonic modes. Our study is the first due step towards the construction and full quantum analysis of an optomechanical machine working fully out of equilibrium.