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 distinguishing even a perfect `NOON' state from a statistical mixture using standard detection methods will present experimental difficulties.
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.
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.
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…
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 study the possible formation of large (mesoscopic) molecular ions in an ultracold degenerate bosonic gas doped with charged particles (ions). We show that the polarization potentials produced by the ionic impurities are capable of capturing hundreds of atoms into loosely bound states. We describe the spontaneous formation of these hollow molecular ions via phonon emission and suggest an optical technique for coherent stimulated transitions of free atoms into a specific bound state. These results open up new interesting possibilities for manipulating tightly confined ensembles.
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 consider how macroscopic quantum superpositions may be created from arrays of Bose-Einstein condensates. We study a system of three condensates in Fock states, all with the same number of atoms and show that this has the form of a highly entangled superposition of different quasi-momenta. We then show how, by partially releasing these condensates and detecting an interference pattern where they overlap, it is possible to create a macroscopic superposition of different relative phases for the remaining portions of the condensates. We discuss methods for confirming these superpositions.
Conventional wisdom is that quantum effects will tend to disappear as the number of quanta in a system increases, and the evolution of a system will become closer to that described by mean field classical equations. In this letter we combine newly developed experimental techniques to propose and analyse an experiment using a Bose-Hubbard trimer where the opposite is the case. We find that differences in the preparation of a centrally evacuated trimer can lead to readily observable differences in the subsequent dynamics which increase with system size. Importantly, these differences can be dete…
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 present a straightforward scheme for creating macroscopic superpositions of different superfluid flow states of Bose-Einstein condensates trapped in optical lattices. This scheme has the great advantage that all the techniques required are achievable with current experiments. Furthermore, the relative difficulty of creating cats scales favorably with the size of the cat. This means that this scheme may be well-suited to creating superpositions involving large numbers of particles. Such states may have interesting technological applications such as making quantum-limited measurements of angu…
We propose a scheme to create a macroscopic ``Schödinger cat'' state formed by two interacting Bose condensates. In analogy with quantum optics, where the control and engineering of quantum states can be maintained to a large extend, we consider the present scheme to be an example of quantum atom optics at work.
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.
We propose a possible scheme for generating spin-J geometric phases using a coupled two-mode Bose-Einstein condensate (BEC). First we show how to observe the standard Berry phase using Raman coupling between two hyperfine states of the BEC. We find that the presence of intrinsic interatomic collisions creates degeneracy in energy that allows implementation of the non-Abelian geometric phases as well. The evolutions produced can be used to produce interference between different atomic species with high numbers of atoms or to fine control the difference in atoms between the two species. Finally,…
We propose a scheme for generation of arbitrary coherent superposition of vortex states in Bose-Einstein condensates (BEC) using the orbital angular momentum (OAM) states of light. We devise a scheme to generate coherent superpositions of two counter-rotating OAM states of light using known experimental techniques. We show that a specially designed Raman scheme allows transfer of the optical vortex superposition state onto an initially non-rotating BEC. This creates an arbitrary and coherent superposition of a vortex and anti-vortex pair in the BEC. The ideas presented here could be extended t…
The multiphoton quantum superposition generated by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging to an EPR entangled pair is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The effect can be greatly enhanced if the mirror is part of a cavity structure or is used within an optical interferometer. The overall process will realize an Entangled Macroscopic Quantum Superposition involving a ''microscopic'' singe-photon state of polarization and the coherent ''macroscopic'' displacement of the BEC structure acting in space-l…
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 …
Matter-wave interferometers are, in principle, orders of magnitude more sensitive than their optical counterparts. Nevertheless, creation of matter-wave currents to achieve such a sensitivity is a continuing challenge. Here, we propose the use of Optical Angular Momentum (OAM) induced vortex superpositions in Bose-Einstein Condensates (BECs) as an alternative to atom interferometers for gyroscopy. The coherent superposition of two counter-rotating vortex states of a trapped condensate leads to an interference pattern that rotates by an angle proportional to the angular velocity of the rotating…
We recently proposed a scheme for the creation of coherent superpositions of vortex states in Bose-Einstein condensates (BEC) using orbital angular momentum (OAM) states of light [Phys. Rev. Lett. 95, 173601 (2005)]. Here we discuss further technical details of the proposal, provide alternative, time-reversal-symmetric scheme for transfer of a superposition of OAM states of light to the BEC via a procedure analogous to the traditional STimulated Raman Adiabatic Passage (STIRAP) technique, and discuss an alternative trap configuration conducive for sustaining large charge vortices. Superpositio…
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…
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…
We theoretically investigate the effect of multi-mode dynamics on the creation of macroscopic superposition states (spin-cat states) in Bose-Einstein condensates via one-axis twisting. A two-component Bose-Einstein condensate naturally realises an effective one-axis twisting interaction, under which an initially separable state will evolve toward a spin-cat state. However, the large evolution times necessary to realise these states is beyond the scope of current experiments. This evolution time is proportional to the degree of asymmetry in the relative scattering lengths of the system, which r…
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…
The condensate number distribution during the transition of a dilute, weakly interacting gas of N=200 bosonic atoms into a Bose-Einstein condensate is modeled within number conserving master equation theory of Bose-Einstein condensation. Initial strong quantum fluctuations occuring during the exponential cycle of condensate growth reduce in a subsequent saturation stage, before the Bose gas finally relaxes towards the Gibbs-Boltzmann equilibrium.
Ultra-cold atoms in light-shaped potentials open up new ways to explore mesoscopic physics: Arbitrary trapping potentials can be engineered with only a change of the laser field. Here, we propose using ultracold atoms in light-shaped potentials to feasibly realize a cold atom device to study one of the fundamental problems of mesoscopic physics, the Aharonov-Bohm effect: The interaction of particles with a magnetic field when traveling in a closed loop. Surprisingly, we find that the Aharonov-Bohm effect is washed out for interacting bosons, while it is present for fermions. We show that our a…
We study how macroscopic superpositions of coherent states produced by the nondissipative dynamics of binary mixtures of ultracold atoms are affected by atom losses. We identify different decoherence scenarios for symmetric or asymmetric loss rates and interaction energies in the two modes. In the symmetric case the quantum coherence in the superposition is lost after a single loss event. By tuning appropriately the energies we show that the superposition can be protected, leading to quantum correlations useful for atom interferometry even after many loss events.
We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a three-mode spinor Bose-Einstein condensate. The ground state is protected by a finite energy gap, is immune to phase noise, and the measurement of the number of particles in one mode heralds the coherent preparation of the two other modes simultaneously empty and filled. Highly entangled macroscopic superposition states are generated with large probability also taking into account quasi-adiabatic preparation of the ground state. All the key ingredients necessary to realize our proposal a…
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 present a scheme for creating macroscopic superpositions of the direction of superfluid flow around a loop. Using the Bose-Hubbard model we study an array of Bose-Einstein condensates trapped in optical potentials and coupled to one another to form a ring. By rotating the ring so that each particle acquires on average half a quantum of superfluid flow, it is possible to create a multiparticle superposition of all the particles rotating and all the particles stationary. Under certain conditions it is possible to scale up the number of particles to form a macroscopic superposition. The simpli…
We consider two dilute gas Bose-Einstein condensates with opposite velocities from which a monochromatic light field detuned far from the resonance of the optical transition is coherently scattered. In the thermodynamic limit, when the relative fluctuations of the atom number difference between the two condensates vanish, the relative phase between the Bose-Einstein condensates may be established in a superposition state by detections of spontaneously scattered photons, even though the condensates have initially well-defined atom numbers. For a finite system, stochastic simulations show that t…
We derive stochastic master equations for a quantum system interacting with a Bose field prepared in a superposition of continuous-mode coherent states. To determine a conditional evolution of the quantum system we use a collision model with an environment given as an infinite chain of not interacting between themselves qubits prepared initially in a entangled state being a discrete analogue of a superposition of coherent states of the Bose field. The elements of the environment chain interact with the quantum system in turn one by one and they are subsequently measured. We determine a conditi…
In a two-mode Bose-Josephson junction formed by a binary mixture of ultracold atoms, macroscopic superpositions of phase states are produced during the time evolution after a sudden quench to zero of the coupling amplitude. Using quantum trajectories and an exact diagonalization of the master equation, we study the effect of one-, two-, and three-body atom losses on the superpositions by analyzing separately the amount of quantum correlations in each subspace with fixed atom number. The quantum correlations useful for atom interferometry are estimated using the quantum Fisher information. We i…
We study why it is quite so hard to make a superposition of superfluid flows in a Bose-Einstein condensate. To do this we initially investigate the quantum states of $N$ atoms trapped in a 1D ring with a barrier at one position and a phase applied around it. We show how macroscopic superpositions can in principle be produced and investigate factors which affect the superposition. We then use the Bose-Hubbard model to study an array of Bose-Einstein condensates trapped in optical potentials and coupled to one another to form a ring. We derive analytic expressions for the quality of the superpos…
For a Bose condensate in a double-well potential or with two Josephson-coupled internal states, the condensate wavefunction is a superposition. Here we consider coupling two such Bose condensates, and suggest the existence of a joint condensate wavefunction, which is in general a superposition of all products of the bases condensate wavefunctions of the two condensates. The corresponding many-body state is a product of such superposed wavefunctions, with appropriate symmetrization. These states may be potentially useful for quantum computation. There may be robustness and stability due to macr…
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 provide a scheme for the generation of entangled number states of Bose-Einstein condensates in multiple wells with cyclic pairwise connectivity. The condensate ground state in a multiple well trap can self-evolve, when phase engineered with specific initial phase differences between the neighboring wells, to a macroscopic superposition state with controllable entanglement -- to multiple well generalization of double well NOON states. We demonstrate through numerical simulations the creation of entangled states in three and four wells and then explore the creation of "larger" entangled state…
In a two-mode Bose Josephson junction the dynamics induced by a sudden quench of the tunnel amplitude leads to the periodic formation of entangled states. For instance, squeezed states are formed at short times and macroscopic superpositions of phase states at later times. The two modes of the junction can be viewed as the two arms of an interferometer; use of entangled states allows to perform atom interferometry beyond the classical limit. Decoherence due to the presence of noise degrades the quantum correlations between the atoms, thus reducing phase sensitivity of the interferometer. We co…
