We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size $S$ of a superposition, with respect to an observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that superposition. Such superpositions are referred to as generalized $S$-scopic superpositions to distinguish them from the extreme superpositions that superpose only the two states that have a difference $S$ in their prediction for the observable. We also consider generalized $S$-scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalized $S$-scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing. We also discuss how the signatures enable a new type of Einstein-Podolsky-Rosen gedanken experiment.
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to "doing quantum electrodynamics while thinking classically," allowing one to substitute esse…
Entanglement between two macroscopic atomic ensembles induced by measurement on an ancillary light system has proven to be a powerful method for engineering quantum memories and quantum state transfer. Here we investigate the feasibility of such methods for generation, manipulation and detection of genuine multipartite entanglement between mesoscopic atomic ensembles. Our results extend in a non trivial way the EPR entanglement between two macroscopic gas samples reported experimentally in [B. Julsgaard, A. Kozhekin, and E. Polzik, Nature {\bf 413}, 400 (2001)]. We find that under realistic co…
It has been shown earlier that matter waves which are known to lie typically in the range of a few Angstrom, can also manifest in the macrodomain with a wave length of a few centimeters, for electrons propagating along a magnetic field. This followed from the predictions of a probability amplitude theory by the author in the classical macrodomain of the dynamics of charged particles in a magnetic field. It is shown in this paper that this case constitutes only a special case of a generic situation whereby composite systems such as atoms and molecules in their highly excited internal states,can…
In this letter the phenomenon of macroscopic quantization is investigated using the particle on the ring interacting with the dissipative environment as an example. It is shown that the phenomenon of macroscopic quantization has the clear physical origin in that case. It follows from the angular momentum conservation combined with momentum quantization for bare particle on the ring . The existence an observable which can take only integer values in the zero temperature limit is rigorously proved. With the aid of the mapping between particle on the ring and Ambegaokar-Eckern-Schon model, which …
We develop criteria sufficient to enable detection of macroscopic coherence where there are not just two macroscopically distinct outcomes for a pointer measurement, but rather a spread of outcomes over a macroscopic range. The criteria provide a means to distinguish a macroscopic quantum description from a microscopic one based on mixtures of microscopic superpositions of pointer-measurement eigenstates. The criteria are applied to Gaussian-squeezed and spin-entangled states.
Quantum decoherence is of primary importance for relaxation to an equilibrium distribution and, accordingly, for equilibrium processes. We demonstrate how coherence breaking implies evolution to a microcanonical distribution (``microcanonical postulate'') and, on that ground, consider an adiabatic process, in which there is no thermostat. We stress its difference from a zero-polytropic process, i.e., a process with zero heat capacity but involving a thermostat. We find the distribution for the adiabatic process and show that (i) in the classical limit this distribution is canonical, (ii) for m…
We examine how to signify and quantify the mesoscopic quantum coherence of approximate two-mode NOON states and spin-squeezed two-mode Bose-Einstein condensates (BEC). We identify two criteria that verify a nonzero quantum coherence between states with quantum number different by $n$. These criteria negate certain mixtures of quantum states, thereby signifying a generalised $n$-scopic Schrodinger cat-type paradox. The first criterion is the correlation $\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle\neq0$ (here $\hat{a}$ and $\hat{b}$ are the boson operators for each mode). The correlation manif…
The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is maximized at equilibrium. We say that the macroscopic systems are extensive and so it is also the entropy. For a mesoscopic system, by definition, the size and the contacts with other systems influence its thermodynamic properties and therefore, if we define an entropy, this cannot be a homogeneous of order one function in the extensive variables. So, mesoscopic …
We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopicquantum- superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges…
The availability of Bose-Einstein condensates as mesoscopic or macroscopic quantum objects has aroused new interest in the possiblity of making and detecting coherent superpositions involving many atoms. In this article we show that it may be possible to generate such a superposition state in a reasonably short time using Feshbach resonances to tune the inter-atomic interactions in a double-well condensate. We also consider the important problem of distinguishing whether a coherent superposition or a statistical mixture is generated by a given experimental procedure. We find that unambiguously…
The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of non-interacting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wavepackets, their time dela…
We investigate the multiphoton states generated by high-gain optical parametric amplification of a single injected photon, polarization encoded as a ''qubit''. The experiment configuration exploits the optimal phase-covariant cloning in the high gain regime. The interference fringe pattern showing the non local transfer of coherence between the injected qubit and the mesoscopic amplified output field involving up to 4000 photons has been investigated. A probabilistic new method to extract full information about the multiparticle output wavefunction has been implemented.
We show a general approach for detecting genuine multipartite entanglement (GME) and partial inseparability in many-body-systems by means of macroscopic observables (such as the energy) only. We show that the obtained criteria, the "GME gap" and "the k-entanglement gap", detect large areas of genuine multipartite entanglement and partial entanglement in typical many body states, which are not detected by other criteria. As genuine multipartite entanglement is a necessary property for several quantum information theoretic applications such as e.g. secret sharing or certain kinds of quantum comp…
A recent experiment [K. C. Lee et al., Science 334, 1253 (2011)] succeeded in detecting entanglement between two macroscopic specks of diamonds, separated by a macroscopic distance, at room temperature. This impressive results is a further confirmation of the validity of quantum theory in (at least parts of) the mesoscopic and macroscopic domain, and poses a challenge to collapse models, which predict a violation of the quantum superposition principle, which is the bigger the larger the system. We analyze the experiment in the light of such models. We will show that the bounds placed by experi…
A mesoscopic system of a few particles exhibits behaviors that strongly differ from those of a macroscopic system. While in a macroscopic system phase transitions are universal, a change in the state of a mesoscopic system depends on its specific properties, like the number of particles, to the point that changes of state can be disfavored for specific magic numbers. A transition that has no counterpart in the macroscopic world is orientational melting, in which localized particles with long-range repulsive interactions forming a two-dimensional crystal become delocalized in common circular or…
Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of th…
The question as to whether or not quantum mechanics is applicable to the macroscopic scale has motivated efforts to generate superposition states of macroscopic numbers of particles and to determine their effective size. Superpositions of circulating current states in flux qubits constitute candidate states that have been argued to be at least mesoscopic. We present a microscopic analysis that reveals the number of electrons participating in these superpositions to be surprisingly but not trivially small, even though differences in macroscopic observables are large.
For the purpose of understanding the quantum behavior such as quantum decoherence, fluctuations, dissipation, entanglement and teleportation of a mesoscopic or macroscopic object interacting with a general environment, we derive here a set of exact master equations for the reduced density matrix of $N$ interacting harmonic oscillators in a heat bath with arbitrary spectral density and temperature. Two classes of problems of interest to us which these equations can be usefully applied to are that of the quantum dynamics of nanoelectromechanical oscillators and the entanglement evolution of mult…
We propose a universal language to assess macroscopic quantumness in terms of coherence, with a set of conditions that should be satisfied by any measure of macroscopic coherence. We link the framework to the resource theory of asymmetry. We show that the quantum Fisher information gives a good measure of macroscopic coherence, enabling a rigorous justification of a previously proposed measure of macroscopicity. This picture lets us draw connections between different measures of macroscopicity and evaluate them; we show that another widely studied measure fails one of our criteria.
Quantum computing implementations under consideration today typically deal with systems with microscopic degrees of freedom such as photons, ions, cold atoms, and superconducting circuits. The quantum information is stored typically in low-dimensional Hilbert spaces such as qubits, as quantum effects are strongest in such systems. It has however been demonstrated that quantum effects can be observed in mesoscopic and macroscopic systems, such as nanomechanical systems and gas ensembles. While few-qubit quantum information demonstrations have been performed with such macroscopic systems, a quan…
We demonstrate a break-down in the macroscopic (classical-like) dynamics of wave-packets in complex microscopic and mesoscopic collisions. This break-down manifests itself in coherent superpositions of the rotating clockwise and anticlockwise wave-packets in the regime of strongly overlapping many-body resonances of the highly-excited intermediate complex. These superpositions involve $\sim 10^4$ many-body configurations so that their internal interactive complexity dramatically exceeds all of those previously discussed and experimentally realized. The interference fringes persist over a time-…
We analyse a proposal that we have recently put forward for an interface between matter-wave and optomechanical technologies from the perspective of macroscopic quantumness. In particular, by making use of a measure of macroscopicity in quantum superpositions that is particularly well suited for continuous variables systems, we demonstrate the existence of working points for our interface at which a quantum mechanical superposition of genuinely mesoscopic states is achieved. Our proposal thus holds the potential to affirm itself as a viable atom-to-mechanics transducer of quantum coherences.
We discuss the conclusions that can be drawn on a recent experimental micro-macro entanglement test [F. De Martini, F. Sciarrino, and C. Vitelli, Phys. Rev. Lett. 100, 253601 (2008). The system under investigation is generated through optical parametric amplification of one photon belonging to an entangled pair. The adopted entanglement criterion makes it possible to infer the presence of entanglement before losses, that occur on the macrostate, under a specific assumption. In particular, an a priori knowledge of the system that generates the micro-macro pair is necessary to exclude a class of…
Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations, that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in between the quantum microscopic scale and the classical macroscopic one. We hereby present the gen…
Relativistic electrons experience very slight wave packet distortion and negligible momentum recoil when interacting with nanometer-sized samples, as a consequence of the ultra-short interaction time. Accordingly, modeling fast electrons as classical point-charges provides extremely accurate theoretical predictions of energy-loss spectra. Here we investigate the aloof interaction of nanometer-sized electron beams of few keV with micron-sized samples, a regime where the classical description generally fails due to significant wavefunction broadening and momentum recoil. To cope with these effec…
The existence of quantum correlations affects both microscopic and macroscopic systems. On macroscopic systems they are difficult to observe and usually irrelevant for the system's evolution due to the frequent energy exchange with the environment. The world-wide network of gravitational-wave (GW) observatories exploits optical as well as mechanical systems that are highly macroscopic and largely decoupled from the environment. The quasi-monochromatic light fields in the kilometre-scale arm resonators have photon excitation numbers larger than $10^{19}$, and the mirrors that are quasi-free fal…
We consider dynamics of a disordered ensemble of qubits interacting with single mode photon field, which is described by exactly solvable inhomogeneous Dicke model. In particular, we concentrate on the crossover from few-qubit systems to the system of many qubits and analyze how collective behavior of coupled qubits-cavity system emerges despite of the broadening. We show that quantum interference effects survive in the mesoscopic regime -- dynamics of an entangled Bell state encoded into the qubit subsystem remains highly sensitive to the symmetry of the total wave function. Moreover, relaxat…
We consider two non-interacting infinite quantum spin chains immersed in a common thermal environment and undergoing a local dissipative dynamics of Lindblad type. We study the time evolution of collective mesoscopic quantum spin fluctuations that, unlike macroscopic mean-field observables, retain a quantum character in the thermodynamical limit. We show that the microscopic dissipative dynamics is able to entangle these mesoscopic degrees of freedom, through a purely mixing mechanism. Further, the behaviour of the dissipatively generated quantum correlations between the two chains is studied …
