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 are specified for observing these features.
We study mesoscopic superpositions of two component Bose-Einstein condensates. Atomic condensates, with long coherence times, are good systems in which to study such quantum phenomenon. We show that the mesoscopic superposition states can be rapidly generated in which the atoms dispersively interact with the photon field in a cavity. We also discuss the production of compass states which are generalized Schrödinger cat states. The physical realization of mesoscopic states is important in studying decoherence and precision measurement.
We propose a method using the dispersive interaction between atoms and a high quality cavity to realize the mesoscopic superposition of coherent states which would exhibit sub-Planck structures in phase space. In particular we focus on a superposition involving four coherent states. We show interesting interferences in the conditional measurements involving two atoms.
Using resonant interaction between atoms and the field in a high quality cavity, we show how to generate a superposition of many mesoscopic states of the field. We study the quasi-probability distributions and demonstrate the nonclassicality of the superposition in terms of the zeroes of the Q-function as well as the negativity of the Wigner function. We discuss the decoherence of the generated superposition state. We propose homodyne techniques of the type developed by Auffeves et al [Phys. Rev. Lett. 91, 230405 (2003)] to monitor the superposition of many mesoscopic states.
We present a strategy to engineer a simple cavity-QED two-bit universal quantum gate using mesoscopic distinct quantum superposition states. The dissipative effect on decoherence and amplitude damping of the quantum bits are analyzed and the critical parameters are presented.
We report the realization of an entangled quantum superposition of M=12 photons by a high gain, quantum-injected optical parametric amplification. The system is found so highly resilient against decoherence to exhibit directly accessible mesoscopic interference effects at normal temperature. By modern tomographic methods the non-separability and the quantum superposition are demonstrated for the overall mesoscopic output state of the dynamic ''closed system''. The device realizes the condition conceived by Erwin Schroedinger with his 1935 paradigmatic ''Cat'' apologue, a fundamental landmark i…
We propose a scheme for the generation and reconstruction of entangled states between the internal and external (motional) degrees of freedom of a trapped electron. Such states also exhibit quantum coherence at a mesoscopic level.
The dynamics of the Jaynes-Cummings Hamiltonian is studied in the semiclassical limit by reducing it to quantum normal form and deriving the phase space dynamics of classically smooth observables. The resulting systematic semiclassical approximation is used to analyze the Rabi oscillations of a photon wave packet revealing subtle consequences of the uncertainty principle.
Here we consider the continuous pumping of a dissipative QED cavity and derive the time-dependent density operator of the cavity field prepared initially as a superposition of mesoscopic coherent states. The control of the coherence of this superposition is analyzed considering the injection of a beam of two-level Rydberg atoms through the cavity. Our treatment is compared to other approaches.
We present a proposal for the production of longer-lived mesoscopic superpositions which relies on two requirements: parametric amplification and squeezed vacuum reservoir for cavity-field states. Our proposal involves the interaction of a two-level atom with a cavity field which is simultaneously subjected to amplification processes.
I consider the interaction of a superposition of mesoscopic coherent states and its approach to a mixed state as a result of a suitably controlled environment. I show how the presence of a gain medium in a cavity can lead to diagonalization in coherent state basis in contrast to the standard model of decoherence. I further show how the new model of decoherence can lead to the generation of $s$ ordered quasi distributions.
Quantum superpositions and entanglement are at the heart of the quantum information science. There have been only a few investigations of these phenomena at the mesoscopic level, despite the fact that these systems are promising for quantum state storage and processing. Here we present two novel experiments with surface plasmons propagating on cm-long metallic stripe waveguides. We demonstrate that two plasmons can be entangled at remote places. In addition, we create a single plasmon in a temporal superposition state: it exists in a superposition of two widely separated moments. These quantum…
We study the generation of superpositions of N00N states by overlapping few-photon-subtracted squeezed vacuum states and coherent states on a 50/50 beam splitter. Assuming parameters that are feasible with current technology results in output states with mean photon numbers of several tens. We show that the generated quantum states violate local realism even in the presence of considerable loss. The occurrence of strong quantum correlations for mesoscopic quantum states of light is particularly beneficial for coupling light and matter quantum systems.
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…
We propose a scalable procedure to generate entangled superpositions of motional coherent states and electronic states in N trapped ions. Beyond their fundamental importance, these states may be of interest for quantum information processing and may be used in experimental studies of decoherence.
We investigate the multiparticle quantum superposition and the persistence of multipartite entanglement of the quantum superposition generated by the quantum injected high-gain optical parametric amplification of a single photon. The physical configuration based on the optimal universal quantum cloning has been adopted to investigate how the entanglement and the quantum coherence of the system persists for large values of the nonlinear parametric gain g.
A phase controlled wave packet, recently used in experiment of wave packet interferometry of adiatomic molecule, is investigated to obtain mesoscopic superposition structures, useful in quantum metrology. This analysis provides a new way of obtaining sub-Planck scale structures at smaller time scale of revival dynamics. We study a number of situations for delineating the smallest interference structures and their control by tailoring the relative phase between two subsidiary wave packets. We also find the most appropriate state, so far, for high precision parameter estimation in a system of di…
We show the feasibility of a tomographic reconstruction of Schrödinger cat states generated according to the scheme proposed by S. Song, C.M. Caves and B. Yurke [Phys. Rev. A 41, 5261 (1990)]. We present a technique that tolerates realistic values for quantum efficiency at photodetectors. The measurement can be achieved by a standard experimental setup.
We propose measurement based conditional generation of superposition of motional states of nanomechanical resonator. We consider a two level quantum mechanical system coupled with nanomechanical resonator through phonon exchange. An interaction, which produces shifts in the state of nanomechanical resonator depending on the state of the qubit, is realized by driving qubit through two resonant lasers. The measurement of the state of quantum mechanical system produces superposition states of nanomechanical resonator. We show that the quantum interference between states in superposition may lead …
A model is presented to describe the recently proposed experiment (J. Raimond, M. Brune and S. Haroche Phys. Rev. Lett {\bf 79}, 1964 (1997)) where a mesoscopic superposition of radiation states is prepared in a high-Q cavity which is coupled to a similar resonator. The dynamical coherence loss of such state in the absence of dissipation is reversible and can in principle be observed. We show how this picture is modified due to the presence of the environmental couplings. Analytical expressions for the experimental conditional probabilities and the linear entropy are given. We conclude that th…
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 super…
We show that continuous real-time feedback can be used to track, control, and protect a mesoscopic superposition of two spatially separated wave-packets. The feedback protocol is enabled by an approximate state-estimator, and requires two continuous measurements, performed simultaneously. For nanomechanical and superconducting resonators, both measurements can be implemented by coupling the resonators to superconducting qubits.
We present a scheme for demonstrating violation of Bell's inequalities using a spin-1/2 system entangled with a pair of classically distinguishable wave packets in a harmonic potential. In the optical domain, such wave packets can be represented by coherent states of a single light mode. The proposed scheme involves standard spin-1/2 projections and measurements of the position and the momentum of the harmonic oscillator system, which for a light mode can be realized by means of homodyne detection. We discuss effects of imperfections, including non-unit efficiency of the homodyne detector, and…
We propose a scheme to create coherent superpositions of annular flow of strongly-interacting bosonic atoms in a 1D ring trap. The non-rotating ground state is coupled to a vortex state with mesoscopic angular momentum by means of a narrow potential barrier and an applied phase that originates from either rotation or a synthetic magnetic field. We show that superposition states in the Tonks-Girardeau regime are robust against single-particle loss due to the effects of strong correlations. The coupling between the mesoscopically distinct states scales much more favorably with particle number th…
We study theoretically the interaction-induced generation of mesoscopic coherent spin state superpositions (small cat states) from an initial coherent spin state in bimodal Bose-Einstein condensates and the subsequent phase revival, including decoherence due to particle losses and fluctuations of the total particle number. In a full multimode description, we propose a preparation procedure of the initial coherent spin state and we study the effect of preexisting thermal fluctuations on the phase revival, and on the spin and orbito-spinorial cat fidelities.
Modeling strongly correlated atoms demonstrates the possibility to prepare quantum superpositions that are robust against experimental imperfections and temperature. Such superpositions of vortex states are formed by adiabatic manipulation of interacting ultracold atoms confined to a one-dimensional ring trapping potential when stirred by a barrier. Here, we discuss the influence of non-ideal experimental procedures and finite temperature. Adiabaticity conditions for changing the stirring rate reveal that superpositions of many atoms are most easily accessed in the strongly-interacting, Tonks-…
Mesoscopic superposition states of photons can be prepared in three cavities interacting with the same two-level atom. By periodically modulating the three cavity frequencies around the transition frequency of the atom with $2π/3$ phase difference, the time reversal symmetry is broken and an optical circulator is generated with chiralities depending on the quantum state of the atom. A superposition of the atomic states can guide photons from one cavity to a mesoscopic superposition of the other two cavities. The physics can be understood in a finite spin-orbit-coupled Fock-state lattice where …
The preparation of mesoscopic states of the radiation and matter fields through atom-field interactions has been achieved in recent years and employed for a range of striking applications in quantum optics. Here we present a technique for the preparation and control of a cavity mode which, besides interacting with a two-level atom, is simultaneously submitted to linear and parametric amplification processes. The role of the amplification-controlling fields in the achievement of real mesoscopic states, is to produce highly-squeezed field states and, consequently, to increase both: i) the distan…
The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The mesoscopic superposition of the generalized cat state is correlated with the corresponding state overlap function, controlled by the sub-Planck structures arising from phase space interference. The asymptotic expression of this overlap function is evaluated and the validity of large phase space support and distinguishability of the constituent states, in which context the asymptotic limit is achieved, are discussed in detail. …
The Josephson junctions (JJs) are at the heart of modern quantum technologies and metrology. In this work we establish quantum features of an atomic soliton Josephson junction (SJJ) device, which consists of two weakly-coupled condensates with negative scattering length. The condensates are trapped in a double-well potential and elongated in one dimension. Starting with classical field theory we map for the first time a two-soliton problem onto the effective two-mode Hamiltonian and perform a second quantization procedure. Compared to the conventional Bosonic Josephson junction (BJJ) condensat…
Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to depend in crucial ways on whether or not an average orthogonality is maintained between reversible Schroedinger dynamics and irreversible processes of diffusion. Moreover, said orthogonality is already in full operation when dealing with a single free Gaussian wave packet. In an application, the quantum mechanical "decay of the wave packet" is shown to simply r…
We consider the degradation of the dynamics of a Gaussian wave packet in a harmonic oscillator under the presence of an environment. This last is given by a single non-degenerate two level system. We analyze how the binary degree of freedom perturbs the free evolution of the wave packet producing decoherence, which is quantified by the Loschmidt Echo. This magnitude measures the reversibility of a perturbed quantum evolution. In particular, we use it here to study the relative "fragility" of coherent superpositions (cat states) with respect to incoherent ones. This fragility or sensitivity tur…
A simple model allows us to study the nonclassical behavior of slowly moving atoms interacting with a quantized field. Atom and field become entangled and their joint state can be identified as a mesoscopic "Schroedinger-cat". By introducing appropriate observables for atom and field and by analyzing correlations between them based on a Bell-type inequality we can show the corresponding nonclassical behavior.
A method for generating a mesoscopic superposition state of the collective spin variable of a gas of atoms is proposed. The state consists of a superposition of the atomic spins pointing in two slightly different directions. It is obtained by using off resonant light to carry out Quantum Non Demolition Measurements of the spins. The relevant experimental conditions, which require very dense atomic samples, can be realized with presently available techniques. Long-lived atomic superposition states may become useful as an off-line resource for quantum computing with otherwise linear operations.
We study decoherence of the external degree of freedom of a tracer particle moving in a one dimensional dilute Boltzmann gas. We find that phase averaging is the dominant decoherence effect, rather than information exchange between tracer and gas particles. While a coherent superposition of two wave packets with different mean positions quickly turns into a mixed state, it is demonstrated that such superpositions of different momenta are robust to phase averaging, until the two wave packets acquire a different position due to the different velocity of each wave packet.
We study the one dimensional time dependent Schrödinger equation for a potential step with $E < V_0$. We obtain the wave is not instantaneously reflected, but for a few moment of time the wave packet penetrate into inaccessible classically region and then reflected. So it is shown that one can write the peneterated wave paket as superposition of incident and reflected wave packets like.
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-…
Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized wave-packet reveals the eigenstates and eigenvalues of the system under consideration. We discuss applications of the wave-packet method in atomic, molecular, and mesoscopic systems and point out specific advantages of the time-dependent approach. In connection with the familiar initial value formulation of classical mechanics, an intuitive interpretation of tran…
While dissipation is widely considered as being harmful for quantum coherence, it can, when properly engineered, lead to the stabilization of non-trivial pure quantum states. We propose a scheme for continuous generation and stabilization of Schrödinger cat states in a cavity using dissipation engineering. We first generate non-classical photon states with definite parity by means of a two-photon drive and dissipation, and then stabilize these transient states against single-photon decay. The single-photon stabilization is autonomous, and is implemented through a second engineered bath, which …
We analyse tunnelling of a single particle, whose initial state is given by a superposition of spatially separated wave packet modes. It is shown that "pile up" of different components the scatterer may change the tunnelling probabilities, making such states a convenient tool for probing the barrier's scattering times. Interference effects arising in resonance tunnelling in are studied in detail. The analysis allows us to gain further insight into the origin of interference effects in scattering of several identical particles.
The revival structure of Stark wave packets is considered. These wave packets have energies depending on two quantum numbers and are characterized by two sets of classical periods and revival times. The additional time scales result in revival structures different from those of free Rydberg wave packets. We show that Stark wave packets can exhibit fractional revivals. We also show that these wave packets exhibit particular features unique to the Stark effect. For instance, the wave functions can be separated into distinct sums over even and odd values of the principal quantum number. These eve…
Within a plane-wave approximation in scattering, an incoming wave packet's Wigner function stays everywhere positive, which obscures such purely quantum phenomena as non-locality and entanglement. With the advent of the electron microscopes with subnanometer-sized beams one can enter a genuinely quantum regime where the latter effects become only moderately attenuated. Here we show how to probe negative values of the Wigner function in scattering of a coherent superposition of two Gaussian packets with a non-vanishing impact-parameter between them (a Schrödinger's cat state) by atomic targets.…
The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of `cat' states, quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their qu…
We first present a summary of recent results concerning the phononic energy transport properties of mesoscopic, suspended dielectric wires. We then discuss some related open problems concerning the fundamental lower limits on the vibrational damping rates of submicron-sized cantilever structures and also the possibility to create and detect quantum superpositions of spatially separated states for such structures.
We find a new phenomenon, a particle like an electron, which transfers kinetic energy to other subject undergoes a decrease in its wave packet size in space and an electron that gains kinetic energy experiences an enlargement of its wavepacket size. This effect occurs in some amount of degree almost in any physical system. The effect has significance on electron transport in semiconductors, quantum wires, future devices in nanotechnology and quantum optics.
Motivated by recent experiments, we consider a Schrödinger cat superposition of two widely separated coherent states in thermal equilibrium. The time development of our system is obtained using Wigner distribution functions. In contrast to our discussion for a two-Gaussian wave packet [Phys. Lett. A 286 (2001) 87], we find that, in the absence of dissipation, the interference term does not decay rapidly in time, but in common with the other two terms, it oscillates in time and persists for all times
We study the dynamics of superposed wave packets in a specific nonlinear Hamiltonian which models the wave packet propagation in Kerr-like media and the dynamics of Bose-Einstein condensates. We show the dependence of initial wave packet superposition on fractional revival times using analysis based on the expectation values, Rényi entropy and Wigner function. We also show how the selective identification of fractional revivals using moments of appropriate observables depends on the number of wave packets present in the initial state.
We observe the quantum coherent dynamics of atomic spinor wavepackets in the double well potentials of a far-off-resonance optical lattice. With appropriate initial conditions the system Rabi oscillates between the left and right localized states of the ground doublet, and at certain times the wavepacket corresponds to a coherent superposition of these mesoscopically distinguishable quantum states. The atom/optical double well potential is a flexible and powerful system for further study of mesoscopic quantum coherence, quantum control and the quantum/classical transition.
We investigate the large-N behaviour of simple examples of supersymmetric interactions for fermions on a lattice. Witten's supersymmetric quantum mechanics and the BCS model appear just as two different aspects of one and the same model. For the BCS model, supersymmetry is only respected in a coherent superposition of Bogoliubov states. In this coherent superposition mesoscopic observables show better stability properties than in a Bogoliubov state.
Coherent manipulation of single-photon wave packets is essentially important for optical quantum communication and quantum information processing. In this paper, we realize controllable splitting and modulation of single-photon-level pulses by using a tripod-type atomic medium. The adoption of two control beams enable us to store one signal pulse into superposition of two distinct atomic collective excitations. By controlling the time delay between the two control pulses, we observe splitting of a stored wave packet into two temporally-distinct modes. By controlling the frequency detuning of t…
We consider the superposition of plane waves and localized wave packets. This kind of wave function can result from a local excitation of a particle described by a plane wave. For charged particles, the wave packet means a current, the time integral of which results in an extra charge, additionally to the one carried by the plane wave. When the duration of the wave packet is too short for its details to be resolved experimentally, it is the extra charge that can be determined and analyzed for information regarding the nature of the interaction that created the wave packet. Assuming that the wa…
We report the experimental demonstration of a controlled-NOT (CNOT) quantum logic gate between motional and internal state qubits of a single ion where, as opposed to previously demonstrated gates, the conditional dynamics depends on the extent of the ion's wave-packet. Advantages of this CNOT gate over one demonstrated previously are its immunity from Stark shifts due to off-resonant couplings and the fact that an auxiliary internal level is not required. We characterize the gate logic through measurements of the post-gate ion state populations for both logic basis and superposition input sta…
We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon d…
In the framework of the paraxial and of the slowly varying envelope approximations, with reference to a normally dispersive medium or to vacuum, the electromagnetic field is given as a continuous quantum superposition of non-dispersive and non-diffracting wave-packets (namely X-waves). Entangled states as pairs of elementary excitations traveling at (approximately) the same velocity are found in optical parametric amplification.
We show that a nano-resonator can be prepared in mesoscopic-superposition states merely by monitoring a qubit coupled to the square of the resonators position. This works for thermal initial states, and does not require a third-order nonlinearity. The required coupling can be generated using a simple open-loop control protocol, obtained with optimal control theory. We simulate the complete preparation process, including environmental noise. Our results indicate the power of open-loop control for state-engineering and measurement in quantum nano-systems.
The potential scattering of electrons carrying non--zero quanta of the orbital angular momentum (OAM) is studied in a framework of the generalized Born approximation, developed in our recent paper by Karlovets \textit{et al.}, Phys. Rev. A. {\textbf 92}, 052703 (2015). We treat these so--called \textit{twisted} electrons as spatially localized wave--packets. The simple and convenient expressions are derived for a number of scattering events in collision of such a vortex electron with a single potential, located at a given impact parameter with respect to the wave-packet's axis. The more realis…
It is proposed that superoscillations play an important role in the interferences which give rise to superluminal effects. To exemplify that, we consider a toy model which allows for a wave packet to travel, in zero time and negligible distortion a distance arbitrarily larger than the width of the wave packet. The peak is shown to result from a superoscillatory superposition at the tail. Similar reasoning applies to the dwell time.
We investigate measurement of electron transport in quantum dot systems by using single-electron transistor as a noninvasive detector. It is demonstrated that such a detector can operate in the ``negative-result measurement'' regime. In this case the measured current is not distorted, providing that it is a non-coherent one. For a coherent transport, however, the possibility of observing a particular state out of coherent superposition leads to distortion of a measured current even in the ``negative-result measurement'' regime. The corresponding decoherence rate is obtained in the framework of…
