Experimental Determination of Irreversible Entropy Production in out-of-Equilibrium Mesoscopic Quantum Systems.

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 micromechanical 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 the 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.

Landauer's Principle in Multipartite Open Quantum System Dynamics.

We investigate the link between information and thermodynamics embodied by Landauer's principle in the open dynamics of a multipartite quantum system. Such irreversible dynamics is described in terms of a collisional model with a finite temperature reservoir. We demonstrate that Landauer's principle holds, for such a configuration, in a form that involves the flow of heat dissipated into the environment and the rate of change of the entropy of the system. Quite remarkably, such a principle for heat and entropy power can be explicitly linked to the rate of creation of correlations among the elements of the multipartite system and, in turn, the non-Markovian nature of their reduced evolution. Such features are illustrated in two exemplary cases.

Irreversibility and the Arrow of Time in a Quenched Quantum System.

Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field. We experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergence, between a microscopic process and its time reversal. Our result addresses the concept of irreversibility from a microscopic quantum standpoint.

Entanglement replication in driven dissipative many-body systems.

We study the dissipative dynamics of two independent arrays of many-body systems, locally driven by a common entangled field. We show that in the steady state the entanglement of the driving field is reproduced in an arbitrarily large series of inter-array entangled pairs over all distances. Local nonclassical driving thus realizes a scale-free entanglement replication and long-distance entanglement distribution mechanism that has immediate bearing on the implementation of quantum communication networks.

Measuring the characteristic function of the work distribution.

We propose an interferometric setting for the ancilla-assisted measurement of the characteristic function of the work distribution following a time-dependent process experienced by a quantum system. We identify how the configuration of the effective interferometer is linked to the symmetries enjoyed by the Hamiltonian ruling the process and provide the explicit form of the operations to implement in order to accomplish our task. We finally discuss two physical settings, based on hybrid optomechanical-electromechanical devices, where the theoretical proposals discussed in our work could find an experimental demonstration.

Experimental distribution of entanglement with separable carriers.

The key requirement for quantum networking is the distribution of entanglement between nodes. Surprisingly, entanglement can be generated across a network without direct transfer-or communication-of entanglement. In contrast to information gain, which cannot exceed the communicated information, the entanglement gain is bounded by the communicated quantum discord, a more general measure of quantum correlation that includes but is not limited to entanglement. Here, we experimentally entangle two communicating parties sharing three initially separable photonic qubits by exchange of a carrier photon that is unentangled with either party at all times. We show that distributing entanglement with separable carriers is resilient to noise and in some cases becomes the only way of distributing entanglement through noisy environments.

Emergent thermodynamics in a quenched quantum many-body system.

We study the statistics of the work done, fluctuation relations, and irreversible entropy production in a quantum many-body system subject to the sudden quench of a control parameter. By treating the quench as a thermodynamic transformation we show that the emergence of irreversibility in the nonequilibrium dynamics of closed many-body quantum systems can be accurately characterized. We demonstrate our ideas by considering a transverse quantum Ising model that is taken out of equilibrium by an instantaneous change of the transverse field.

Experimental quantum networking protocols via four-qubit hyperentangled Dicke states.

We report the experimental demonstration of two quantum networking protocols, namely quantum 1→3 telecloning and open-destination teleportation, implemented using a four-qubit register whose state is encoded in a high-quality two-photon hyperentangled Dicke state. The state resource is characterized using criteria based on multipartite entanglement witnesses. We explore the characteristic entanglement-sharing structure of a Dicke state by implementing high-fidelity projections of the four-qubit resource onto lower-dimensional states. Our work demonstrates for the first time the usefulness of Dicke states for quantum information processing.

Quantum discord bounds the amount of distributed entanglement.

The ability to distribute quantum entanglement is a prerequisite for many fundamental tests of quantum theory and numerous quantum information protocols. Two distant parties can increase the amount of entanglement between them by means of quantum communication encoded in a carrier that is sent from one party to the other. Intriguingly, entanglement can be increased even when the exchanged carrier is not entangled with the parties. However, in light of the defining property of entanglement stating that it cannot increase under classical communication, the carrier must be quantum. Here we show that, in general, the increase of relative entropy of entanglement between two remote parties is bounded by the amount of nonclassical correlations of the carrier with the parties as quantified by the relative entropy of discord. We study implications of this bound, provide new examples of entanglement distribution via unentangled states, and put further limits on this phenomenon.

Photon production from the vacuum close to the superradiant transition: linking the dynamical Casimir effect to the Kibble-Zurek mechanism.

The dynamical Casimir effect (DCE) predicts the generation of photons from the vacuum due to the parametric amplification of the quantum fluctuations of an electromagnetic field. The verification of such an effect is still elusive in optical systems due to the very demanding requirements of its experimental implementation. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way to an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of the DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition.

Self-cooling of a micromirror by radiation pressure.

Cooling of mechanical resonators is currently a popular topic in many fields of physics including ultra-high precision measurements, detection of gravitational waves and the study of the transition between classical and quantum behaviour of a mechanical system. Here we report the observation of self-cooling of a micromirror by radiation pressure inside a high-finesse optical cavity. In essence, changes in intensity in a detuned cavity, as caused by the thermal vibration of the mirror, provide the mechanism for entropy flow from the mirror's oscillatory motion to the low-entropy cavity field. The crucial coupling between radiation and mechanical motion was made possible by producing free-standing micromirrors of low mass (m approximately 400 ng), high reflectance (more than 99.6%) and high mechanical quality (Q approximately 10,000). We observe cooling of the mechanical oscillator by a factor of more than 30; that is, from room temperature to below 10 K. In addition to purely photothermal effects we identify radiation pressure as a relevant mechanism responsible for the cooling. In contrast with earlier experiments, our technique does not need any active feedback. We expect that improvements of our method will permit cooling ratios beyond 1,000 and will thus possibly enable cooling all the way down to the quantum mechanical ground state of the micromirror.

Cold-atom-induced control of an optomechanical device.

We consider a cavity with a vibrating end mirror and coupled to a Bose-Einstein condensate. The cavity field mediates the interplay between mirror and collective oscillations of the atomic density. We study the implications of this dynamics and the possibility of an indirect diagnostic. Our predictions can be observed in a realistic setup that is central to the current quest for mesoscopic quantumness.

Quantum work statistics and resource theories: Bridging the gap through Rényi divergences.

The work performed on or extracted from a nonautonomous quantum system described by means of a two-point projective-measurement approach is a stochastic variable. We show that the cumulant generating function of work can be recast in the form of quantum Rényi-α divergences, and by exploiting the convexity of this cumulant generating function, derive a single-parameter family of bounds for the first moment of work. Higher order moments of work can also be obtained from this result. In this way, we establish a link between quantum work statistics in stochastic approaches and resource theories for quantum thermodynamics, a theory in which Rényi-α divergences take a central role. To explore this connection further, we consider an extended framework involving a control switch and an auxiliary battery, which is instrumental to reconstructing the work statistics of the system. We compare and discuss our bounds on the work distribution to findings on deterministic work studied in resource-theoretic settings.

Thermal transport in out-of-equilibrium quantum harmonic chains.

We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the oscillators, establishing rigorous analytical conditions for the existence of a steady state, whose features we analyze carefully. In particular, we assess the conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction and highlight how such a possibility depends on the environment linked to our system.

Selective effects of thyroid hormonal deprivation on growth and development of olfactory receptor sheet during the early postnatal period: a morphometric and cell count study in the rat.

Light microscopic numerical and morphometric studies were conducted on the olfactory epithelium of postnatal normal and hypothyroid rats. The normal rat olfactory epithelium undergoes marked growth and development during the suckling period (days 1-25): thickness, 50%; area, x 8, total number of olfactory neurons, basal and supporting cells, x 10, x 11 and x 8, respectively. The effects of thyroid hormonal deprivation on these proliferative postnatal growth changes were studied by adding PTU (n-propylthiouracil, a reversible antithyroid goitrogen) to the litter's drinking water from birth to weaning (day 25). The general architecture of naso-olfactory cavities as well as the histology and thickness of the olfactory epithelium were unaffected in the hypothyroid pups. However, the surface area of the olfactory receptor sheet was reduced by 40%, the reduction occurring throughout the cavity, though not uniformly. The total number of olfactory neurons, supporting and basal cells were reduced by 33, 45 and 47%, respectively. These results indicate that the postnatal vertical accretion of olfactory neurons occurring across the epithelial thickness is unaffected in the hypothyroid pups, while the horizontal proliferation of neurons accompanying the expansion of the sheet's surface area is markedly reduced. The results suggest differential effects of thyroid hormones on these modes of proliferative growth and imply further that in addition to possible direct effects, the influence of thyroid hormones on developmental growth of the olfactory epithelial sheets may be secondary to effects on the underlying submucosal connective tissue.

Lack of thyroid hormones but not their excess affects the maturation of olfactory receptor neurons: a quantitative morphologic study in the postnatal rat.

To study quantitatively actions of thyroid hormones on maturation of olfactory receptor neurons (ORN), surface density and total number of receptor knobs (1 knob/ORN) were measured in 1 mu sections from septal olfactory epithelium of newborn, 12- and 25 day normal, hypo- and hyperthyroid rats. Hypothyroidism was induced by adding to drinking water n-propylthiouracil (0.1% w/v) from birth. Hyperthyroidism was induced by daily injection of pups with T4 (1-thyroxine, 0.3 microgram/g b.w., s.c.). Experimental pups showed all the signs of hypo- and hyperthyroidism. Between days 1-25, normal pups showed marked increase in surface area of septal olfactory epithelium (6x), total number (12x) and surface density (#/mm2, 2x) of mature ORNs. Thyroid deficient rats showed, by day 12, marked reductions in epithelial surface area and total number of mature ORNs; these and the surface density deficits became very pronounced by 25 day (30% area, 27% density, 47% # mature ORNs). Hyperthyroid rats, however, did not show an increase in any of these parameters over controls. Although total number of ORNs (mature and immature), as measured by number of nuclei, was also reduced in hypothyroid pups, surface density was not altered, indicating that maturation of ORNs, but not their local accretion is altered in thyroid deficiency. The results indicate that thyroid hormones are essential for normal proliferative expansion of olfactory epithelium and for maturation of ORNs postnatally. These actions of thyroid hormones are not increased or accelerated by excess T4 suggesting saturation of the hormone receptor system at the normal plasma level.

Essential role of thyroid hormones in maturation of olfactory receptor neurons: an immunocytochemical study of number and cytoarchitecture of OMP-positive cells in developing rats.

Neurogenesis and proliferation of olfactory receptor neurons (ORNs) in the olfactory epithelium (OE) are reduced in postnatal hypothyroid rats and upregulated following restoration of thyroid function, leading to compensatory growth and restitution of these deficits [Paternostro M.A. and Meisami E. (1993). Dev. Brain Res. 76, 151-161; Paternostro M.A. and Meisami E. (1994). Dev. Brain Res. 83, 151-162]. To investigate thyroid hormonal role on maturation of ORNs, serial sections of the septal OE from normal newborn, 25- and 90-day-old rats were immunostained for olfactory marker protein (OMP), a marker for mature ORNs, and compared with the same from age-matched hypothyroid rats and those allowed to recover from thyroid deficiency at the time of weaning (day 25). The parameters studied were the localization and distribution of the OMP(+) cells within the OE and their density and total number. Hypothyroidism was induced by adding the reversible goitrogen propylthiouracil (PTU) to the rats' drinking water (1 g/l) from birth to days 25 or 90. Recovery from hypothyroidism was induced by withdrawal of PTU at day 25. The OMP(+) cells occupied a distinct, broad band in the normal rat OE, while in hypothyroid animal, this band was narrow and restricted to OE's apical zones. Recovery resulted in broadening of the OMP(+) cell band and normalized distribution of OMP(+) cells as evident in the 90-day-old recovery animals. In normal control rats, density of OMP(+) cells increased by 2.5- and 1.3-fold during the suckling and post-weaning period (days 25-90), while total numbers of these cells increased by 12- and 3-fold, respectively, during the same age periods. Hypothyroidism decreased the growth in density by 25 and 30%, while total number of OMP(+) neurons were reduced by 40 and 70% in the 25- and 90-day-old animals, respectively. Withdrawal of PTU resulted in marked restoration of these deficits so that, at 90 days, the total number of OMP(+) cells were only 20% less than 90-day-old controls. These results indicate that thyroid hormones are essential for maturation of single ORNs and accretion of new mature ORNs in the OE of suckling and post-weaning rat. Also, the process of maturation and the final number of mature ORNs show remarkable recovery from hypothyroid-induced growth retardation.

Developmental plasticity of the rat olfactory receptor sheet as shown by complete recovery of surface area and cell number from extensive early hypothyroid growth retardation.

To assess the effects of early thyroid deficiency, and recovery from this condition on growth and development of olfactory epithelium (OE), male Sprague-Dawley rat pups were rendered hypothyroid by addition of propylthiouracil (PTU) to their drinking water from birth. At weaning some rats continued to receive PTU while others ere allowed to recover by withdrawal of PTU. Body weights and plasma thyroxine levels were determined in all groups. At the ages of 25, 50 and 90 days, the OE of these hypothyroid and 'recovery' rats were compared with age-matched controls for surface area, epithelial thickness, density and total number of olfactory receptor neurons, basal cells and supporting cells, using morphometric and cell counting methods. Normal rats showed marked and highly significant increases in the OE surface area and olfactory neuron number (2.6- and 2.3-folds) during the post-weaning period. In the hypothyroid rats, body growth and thyroxine levels were severely suppressed. The OE in the 25-day-old hypothyroid rats showed more than 40% reduction in surface area and cell number, compared to controls, but mean epithelial thickness and surface density of cells were unchanged. In the post-weaning hypothyroid rats, the expansion of surface area was severely retarded, and increase in cell number ceased entirely. In rats allowed to recover by PTU withdrawal, by 90 days of age, body weight and size had markedly increased but had not caught up completely; however, thyroxine levels were restored to normal and the surface area and cell number in the OE had increased in a compensatory manner, completely restoring the deficiencies in OE growth, including surface area, numbers of receptor neurons, basal cells and supporting cells. The results indicate marked growth plasticity of OE in the post-weaning rats. This pronounced ability to recover from early growth retardation contrasts with that seen in central neural structures, and indicates the great potential of OE for use as a model neural system for the study of recovery from early damage and growth retardation.

Quantitative [3H]thymidine autoradiography of neurogenesis in the olfactory epithelium of developing normal, hypothyroid and hypothyroid-rehabilitated rats.

We recently reported that postnatal hypothyroidism results in marked reduction in surface area and cell number in the rat olfactory epithelium (OE) and recovery from this condition is accompanied by compensatory growth and restitution of these parameters. To explore the correlative changes in olfactory neurogenesis, i.e. mitotic activity of basal cells (BCs) and migration and survival of developing olfactory receptor neurons (ORNs), hypothyroid rats at postnatal (P) days of P10, P25 and P75 were injected with [3H]thymidine and OE was examined by quantitative autoradiography to determine the density of labeled nuclei at the BC and ORN zones at days 1, 5 and 15 post-injection. These data were compared with those of age-matched controls as well as young adult rats allowed to recover from hypothyroidism at the end of the suckling period (P25). Hypothyroidism was induced by administration of propylthiouracil (PTU) from birth in the drinking water (1 g/l) for 10, 25 and 90 days; recovery was induced by withdrawal of PTU at P25. The results indicated that the densities of labeled nuclei in the BC and ORN zones were not significantly altered in the suckling hypothyroid rats. In the P75 hypothyroid rats density of labeled BC nuclei was unaffected 1 day after injection but was significantly (36%) more than controls 5 days after injection; the density of neuronal nuclei in the ORN zone of P75 injected rats was markedly and significantly reduced (56% and 37% at 5- and 15-days post-injection). Data indicate that mitotic activity of BCs and their migration into the ORN zone is not affected in the hypothyroid infant rats but migration and/or survival of developing ORNs are markedly reduced in the postweaning growing rats made hypothyroid from birth. In rats allowed to recover from hypothyroidism at P25 and injected with labeled thymidine at P75, the density of labeled BC nuclei were significantly increased (48% and 43% at 1- and 5-days post-injection) compared to normal rats suggesting elevated levels of neurogenesis; density of ORN nuclei, however, were the same as controls. The results indicate critical regulatory influences of thyroid hormones on olfactory neurogenesis in the rat olfactory receptor sheet, in particular during the postweaning period.

Marked restoration of density and total number of mature (knob-bearing) olfactory receptor neurons in rats recovering from early hypothyroid-induced growth retardation.

Our recent studies have shown that restoration of thyroid function in developing hypothyroid rats results in upregulation of olfactory neurogenesis and compensatory proliferation of olfactory receptor neurons (ORN) in the olfactory epithelium (OE) (Paternostro and Meisami, Dev. Brain Res., 76 (1993) 151-161; ibid., 83 (1994) 151-162). It was not clear, however, whether the newly forming ORNs undergo complete maturational stages. To determine the effects of restoration of thyroid function on maturation of ORNs, the density and total number of mature ORNs were estimated in the OE of euthyroid and hypothyroid rats at postnatal days 1, 12, 25 and 90 and the results were compared with those in rats allowed to recover from early thyroid deficiency at weaning (day 25). As a marker for mature ORNs, and on the basis of one olfactory dendritic knob per ORN, the density and total number of the olfactory knobs were determined in the entire extent of the OE covering the nasal septum. Hypothyroidism was induced by adding propylthiouracil (PTU) to the drinking water (1 g/l) from birth until days 12, 25 or 90 of age. Recovery from hypothyroidism was induced by withdrawal of PTU at day 25, leading to restoration of thyroid function and somatic growth recovery. The density of olfactory knobs was determined in 1 microm semi-thin sections stained with toluidine blue. In the normal rats, the number of olfactory knobs (= mature ORNs) increased 8.5- and 3-fold during postnatal days 1-25 and 25-90 respectively, reaching a mean value of 4 X 10(6)/septal OE, compared to 2.8- and 1.4-fold, respectively, for the hypothyroid rats. This led to deficits of 51% and 76% in the number of mature ORNs in the 25- and 90-day-old hypothyroid rats. In rats allowed to recover, the number of mature ORNs increased 4.5-fold during postnatal days 25-90 (3 X > hypothyroid rats and 1.5 X > controls). The results indicate marked upregulation of the maturational process of the ORNs and their compensatory accretion within the OE of the recovery group. The recovery process was not complete however, as indicated by a remaining deficit of about 25% in the total number of mature ORN, compared to normal 90-day controls. Thus thyroid hormones are essential for accretion of new mature ORNs in both the suckling and postweaning rats. Also, the ORNs show a remarkable ability to recover from severe early hypothyroid-induced growth retardation and attain normal mature state.