We propose and analyse a practically implementable scheme to generate macroscopic entanglement of a Bose-Einstein condensate in a micro-magnetic trap magnetically coupled to a superconducting loop. We treat the superconducting loop in a quantum superposition of two different flux states coupled with the magnetic trap to generate macroscopic entanglement. Our scheme also provides a platform to realise interferometry of entangled atoms through the Bose-Einstein condensate and to explore physics at the quantum-classical interface.
We present a scheme for creating quantum entangled atomic states through the coherent spin-exchange collision of a spinor Bose-Einstein condensate. The state generated possesses macroscopic Einstein-Podolsky-Roson correlation and the fluctuation in one of its quasi-spin components vanishes. We show that an elongated condensate with large aspect ratio is most suitable for creating such a state.
We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which allows one to explore the interface of quantum optics and condensed matter physics. We propose an experiment where easily detectable atomic spin-flips are induced by the cantilever motion. This can be used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as realized in recent experiments, the backaction of the atoms onto the cantilever is sign…
Entanglement-based technologies, such as quantum information processing, quantum simulations, and quantum-enhanced metrology, have the potential to revolutionise our way of computing and measuring and help clarifying the puzzling concept of entanglement itself. Ultracold atoms on atom chips are attractive for their implementation, as they provide control over quantum systems in compact, robust, and scalable setups. An important tool in this system is a potential depending on the internal atomic state. Coherent dynamics in this potential combined with collisional interactions allows entanglemen…
Using Optimal Control Theory (OCT), we design fast ramps for the controlled transport of Bose-Einstein condensates with atom chips' magnetic traps. These ramps are engineered in the context of precision atom interferometry experiments and support transport over large distances, typically of the order of 1 mm, i.e. about 1,000 times the size of the atomic clouds, yet with durations not exceeding 200 ms. We show that with such transport durations of the order of the trap period, one can recover the ground state of the final trap at the end of the transport. The performance of the OCT procedure i…
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.
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…
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…
Quantum computation using qubits made of two component Bose-Einstein condensates (BECs) is analysed. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in gate operations that can be performed at a macroscopically large energy scale. The large energy scale of the gate operations results in quantum algorithms that may be executed at a time reduced by a factor of N, where N is the number of bosons per qubit. The encoding of the qubits allows for no intrinsic penalty on decoherence times. We illustrate the scheme by an application to Deutsch's and Grover's …
A high-resolution projection and imaging system for ultracold atoms is implemented using a compound silicon and glass atom chip. The atom chip is metalized to enable magnetic trapping while glass regions enable high numerical aperture optical access to atoms residing in the magnetic trap about 100 microns below the chip surface. The atom chip serves as a wall of the vacuum system, which enables the use of commercial microscope components for projection and imaging. Holographically generated light patterns are used to optically slice a cigar-shaped magnetic trap into separate regions; this has …
We theoretically study macroscopic entanglement between a magnetically trapped Bose-Einstein condensate and a superconducting loop. We treat the superconducting loop in a quantum superposition of two different flux states coupling with the magnetic trap to generate macroscopic entanglement. The scheme also provides a platform to investigate interferometry with an entangled Bose Einstein condensate and to explore physics at the quantum-classical interface.
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…
We consider spherically trapped Bose gases in three dimensions with contact interactions, and investigate whether the Bose-Einstein condensate at zero temperature is stable against macroscopic fragmentation into a small number of mutually incoherent pieces. Our results are expressed in terms of a dimensionless interaction measure proportional to the Thomas-Fermi parameter. It is shown that while three-dimensional condensates are inherently much more stable against macroscopic fragmentation than their quasi-one- and quasi-two-dimensional counterparts, they fragment at a sufficiently large value…
We propose an experimental scheme to detect macroscopic Klein tunneling with spin-orbit coupled Bose-Einstein condensates (BECs). We show that a nonlinear Dirac equation with tunable parameters can be realized with such BECs. %in a simple configuration to generate the artificial spin-orbit coupling. Through numerical calculations, we demonstrate that macroscopic Klein tunneling can be clearly detected under realistic conditions. Macroscopic quantum coherence in such relativistic tunneling is clarified and a BEC with a negative energy is shown to be able to transmit transparently through a wide…
Spontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot treat phase off-diagonal effects, and thus not explain Bell inequality violations. We describe another situation that is beyond a SSB treatment: an experiment where particles from two (possibly macroscopic) condensate sources are used for conjugate measurements of the relative phase and populations. Off-diagonal phase effects are characterized by a "quantum angle" and observed via "population oscillations", signaling quantum interference of macroscopically distinct states (QIMDS).
There exists a large number of experimental and theoretical results supporting the picture of "macroscopic qubits" implemented, for instance, by Rydberg atoms, Josephson junctions or Bose-Einstein condensates - the systems which should rather emerge in localized semiclassical states. In this note it is shown how, under realistic conditions, the false qubit interpretation can be consistent with the restricted set of experimental data collected for semiclassical systems. The recent experiments displaying semiclassical character of Bose-Einstein condensates and possible quantumness tests for a si…
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…
We present a detailed theoretical analysis of the implementation of shortcut-to-adiabaticity protocols for the fast transport of neutral atoms with atom chips. The objective is to engineer transport ramps with durations not exceeding a few hundred milliseconds to provide metrologically-relevant input states for an atomic sensor. Aided by numerical simulations of the classical and quantum dynamics, we study the behavior of a Bose-Einstein condensate in an atom chip setup with realistic anharmonic trapping. We detail the implementation of fast and controlled transports over large distances of se…
A new method is used to investigate the tunneling between two weakly-linked Bose-Einstein condensates confined in double-well potential traps. The nonlinear interaction between the atoms in each well contributes to a finite chemical potential, which, with consideration of periodic instantons, leads to a remarkably high tunneling frequency. This result can be used to interpret the newly found Macroscopic Quantum Self Trapping (MQST) effect. Also a new kind of first-order crossover between different regions is predicted.
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.
A Bose-Einstein condensate with attractive interaction can be metastable if it is spatially confined and if the number of condensate bosons $N_0$ is below a certain critical value $N_{\rm c}$. By applying a variational method and the instanton techinique to the Gross-Pitaevskii energy functional, we find analytically the frequency of the collective excitation and the rate of macroscopic quantum tunneling (MQT). We show that near the critical point the tunneling exponent vanishes according to $(1-N_0/N_c)^\frac{5}{4}$ and that MQT can be a dominant decay mechanism of the condensate for $N_0$ ve…
An optical cavity enhances the interaction between atoms and light, and the rate of coherent atom-photon coupling can be made larger than all decoherence rates of the system. For single atoms, this strong coupling regime of cavity quantum electrodynamics (cQED) has been the subject of spectacular experimental advances, and great efforts have been made to control the coupling rate by trapping and cooling the atom towards the motional ground state, which has been achieved in one dimension so far. For N atoms, the three-dimensional ground state of motion is routinely achieved in atomic Bose-Einst…
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 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…
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…
We consider a macroscopic spin qubit based on spin-orbit coupled Bose-Einstein condensates, where, in addition to the spin-orbit coupling, spin dynamics strongly depends on the interaction between particles. The evolution of the spin for freely expanding, trapped, and externally driven condensates is investigated. For condensates oscillating at the frequency corresponding to the Zeeman splitting in the synthetic magnetic field, the spin Rabi frequency does not depend on the interaction between the atoms since it produces only internal forces and does not change the total momentum. However, int…
By utilizing Bose-Einstein condensate solitons, optically manipulated and trapped in a double-well potential, coupled through nonlinear Josephson effect, we propose novel quantum metrology applications with two soliton qubit states. In addition to steady-state solutions in different scenarios, phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes. Schrödinger-cat states, maximally path-entangled ($N00N$) states, and macroscopic soliton qubits are predicted and exploited for the distinguish…
The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the quantum dynamics of lattice spin systems. Such general bounds are not available for most bosonic lattice gases due to their unbounded local interactions. Here we establish for the first time a general ballistic upper bound on macroscopic particle transport in the paradigmatic Bose-Hubbard model. The bound is the first to cover a broad class of initial states with positive density including Mott states, which resolves a longstanding open problem. It applies to Bose-Hubbard type models on any lattice with not to…
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.
A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking.
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…
Spin coherent states are the matter equivalent of optical coherent states, where a large number of two component particles form a macroscopic state displaying quantum coherence. Here we give a detailed study of entanglement generated between two spin-1/2 BECs due to an Sz1 Sz2 interaction. The states that are generated show a remarkably rich structure showing fractal characteristics. In the limit of large particle number N, the entanglement shows a strong dependence upon whether the entangling gate times are a rational or irrational multiple of pi/4. We discuss the robustness of various states…
A fully developed Bose-Einstein condensate, containing macroscopically large number of bosons can under certain conditions be considered as a generalized vacuum state. Applying the annihilation operator to the condensate, hole states can be defined. Infinite ladders of such hole states can be considered as generalized coherent states of the creation operator. Dedicated to the memory of V. N. Gribov.
The EPR argument points to the existence of additional variables that are necessary to complete standard quantum theory. It was dismissed by Bohr because it attributes physical reality to isolated microscopic systems, independently of the macroscopic measurement apparatus. Here, we transpose the EPR argument to macroscopic systems, assuming that they are in spatially extended Fock spin states and subject to spin measurements in remote regions of space. Bohr's refutation of the EPR argument does not seem to apply in this case, since the difference of scale between the microscopic measured syste…
Quantum phenomena appear in a macroscopic scale in Bose-Einstein condensates. The Gross-Pitaevskii (GP) equation describes the dynamics of the weakly interacting Bose-Einstein condensates. The GP equation has a form of the Schroedinger equation with self-interaction. The coupled Gross-Pitaevskii equations are used to describe some mixtures of Bose-Einstein condensates. In this paper, we will show some numerical results of coupled Gross-Pitaevskii equations without self-interaction, which has a form of nonlinearly-coupled Schroedinger equations. We demonstrate that the macroscopic oscillation a…
We consider an ultracold quantum degenerate gas in an optical lattice inside a cavity. This system represents a simple but key model for "quantum optics with quantum gases," where a quantum description of both light and atomic motion is equally important. Due to the dynamical entanglement of atomic motion and light, the measurement of light affects the many-body atomic state as well. The conditional atomic dynamics can be described using the Quantum Monte Carlo Wave Function Simulation method. In this paper, we emphasize how this usually complicated numerical procedure can be reduced to an ana…
The ground state of Bose-Einstein condensates with attractive particle interaction is metastable. One of the decay mechanisms of the condensate is a collapse by macroscopic quantum tunneling, which can be described by the bounce trajectory as solution of the time-dependent Gross-Pitaevskii equation in imaginary time. For condensates with an electromagnetically induced gravity-like interaction the bounce trajectory is computed with an extended variational approach using coupled Gaussian functions and simulated numerically exact within the mean-field approach on a space-time lattice. It is shown…
We study the stability of attractive atomic Bose-Einstein condensate and the macroscopic quantum many-body tunneling (MQT) in the anharmonic trap. We utilize correlated two-body basis function which keeps all possible two-body correlations. The anharmonic parameter ($λ$) is slowly tuned from harmonic to anharmonic. For each choice of $λ$ the many-body equation is solved adiabatically. The use of the van der Waals interaction gives realistic picture which substantially differs from the mean-field results. For weak anharmonicity, we observe that the attractive condensate gains stability with lar…
We resolve the real-time dynamics of a purely dissipative $s = 1/2$ quantum spin or, equivalently, hard-core boson model on a hypercubic $d$-dimensional lattice. The considered quantum dissipative process drives the system to a totally symmetric macroscopic superposition in each of the $S^3$ sectors. Different characteristic time scales are identified for the dynamics and we determine their finite-size scaling. We introduce the concept of cumulative entanglement distribution to quantify multiparticle entanglement and show that the considered protocol serves as an efficient method to prepare a …
We combine the ideas of dressed Bose-Einstein condensates, where an intracavity optical field allows one to design coupled, multicomponent condensates, and of dark states of quantum systems, to generate a full quantum entanglement between two matter waves and two optical waves. While the matter waves are macroscopically populated, the two optical modes share a single photon. As such, this system offers a way to influence the behaviour of a macroscopic quantum system via a microscopic ``knob''.
Squeezed states and macroscopic superpositions of coherent states have been predicted to be generated dynamically in Bose Josephson junctions. We solve exactly the quantum dynamics of such a junction in the presence of a classical noise coupled to the population-imbalance number operator (phase noise), accounting for, for example, the experimentally relevant fluctuations of the magnetic field. We calculate the correction to the decay of the visibility induced by the noise in the non-Markovian regime. Furthermore, we predict that such a noise induces an anomalous rate of decoherence among the c…
We review our recent and ongoing work with Fermi gases on an atom chip. After reviewing some statistical and thermodynamic properties of the ideal, non-interacting Fermi gas, and a brief description of our atom chip and its capabilities, we discuss our experimental approach to producing a potassium-40 degenerate Fermi gas (DFG) using sympathetic cooling by a rubidium-87 Bose-Einstein condensate on an atom chip. In doing so, we describe the factors affecting the loading efficiency of the atom chip microtrap. This is followed by a discussion of species selectivity in radio frequency manipulation…
It is shown that bifurcations of the mean-field dynamics of a Bose-Einstein condensate can be related with the quantum phase transitions of the original many-body system. As an example we explore the intra-band tunneling in the two-dimensional optical lattice. Such a system allows for easy control by the lattice depth as well as for macroscopic visualization of the phase transition. The system manifests switching between two selftrapping states or from a selftrapping state to a superposition of the macroscopically populated selftrapping states with the step-like variation of the control parame…
Two component (spinor) Bose-Einstein condensates (BECs) are considered as the nodes of an interconnected quantum network. Unlike standard single-system qubits, in a BEC the quantum information is duplicated in a large number of identical bosonic particles, thus can be considered to be a "macroscopic" qubit. One of the difficulties with such a system is how to effectively interact such qubits together in order to transfer quantum information and create entanglement. Here we propose a scheme of cavities containing spinor BECs coupled by optical fiber in order to achieve this task. We discuss ent…
In this paper we explore the rich structure of macroscopic many-particle quantum states for Bose- Einstein condensate in an optical cavity with the tunable nonlinear atom-photon interaction [Nature (London) 464, 1301 (2010)]. Population inversion, bistable normal phases and the coexistence of normal{superradiant phases are revealed by adjusting of the experimentally realizable interaction strength and pump-laser frequency. For the negative (effective) cavity-frequency we observe remark- ably an inverted quantum phase transition (QPT) from the superradiant to normal phases with the increase of …
We have fabricated and tested an atom chip that operates as a matter wave interferometer. In this communication we describe the fabrication of the chip by ion-beam milling of gold evaporated onto a silicon substrate. We present data on the quality of the wires, on the current density that can be reached in the wires and on the smoothness of the magnetic traps that are formed. We demonstrate the operation of the interferometer, showing that we can coherently split and recombine a Bose-Einstein condensate with good phase stability.
We introduce a method for the dissipative preparation of strongly correlated quantum states of ultracold atoms in an optical lattice via localized particle loss. The interplay of dissipation and interactions enables different types of dynamics. This ushers a new line of experimental methods to maintain the coherence of a Bose-Einstein condensate or to deterministically generate macroscopically entangled quantum states.
We discuss and model an experiment to study quasi-condensate growth on an atom chip. In particular, we consider the addition of a deep dimple to the weak harmonic trap confining an ultracold one-dimensional atomic Bose gas, below or close to the characteristic temperature for quasi-condensate formation. The subsequent dynamics depends critically on both the initial conditions, and the form of the perturbing potential. In general, the dynamics features a combination of shock-wave propagation in the quasi-condensate, and quasi-condensate growth from the surrounding thermal cloud.
It is well-known that increasing the nonlinearity due to repulsive atomic interactions in a double-well Bose-Einstein condensate suppresses quantum tunnelling between the two sites. Here we find analogous behaviour in the dynamical tunnelling of a Bose-Einstein condensate between period-one resonances in a single driven potential well. For small nonlinearities we find unhindered tunnelling between the resonances, but with an increasing period as compared to the non-interacting system. For nonlinearities above a critical value we generally observe that the tunnelling shuts down. However, for ce…
We consider a weakly interacting coherently coupled Bose-Einstein condensate in a double-well potential. We show by means of stochastic simulations that the system could possibly be driven to an entangled macroscopic superposition state or a Schrödinger cat state by means of a continuous quantum measurement process.
We propose a double-well configuration for optical trapping of ultracold two-species Fermi-Bose atomic mixtures. Two signatures of macroscopic quantum coherence attributable to a superfluid phase transition for the Fermi gas are analyzed. The first signature is based upon tunneling of Fermi pairs when the power of the deconfining laser beam is significantly reduced. The second relies on the observation of interference fringes in a regime where the fermions are trapped in two sharply separated minima of the potential. Both signatures rely on small decoherence times for the Fermi samples, which …
We present a quantum phase space model of Bose-Einstein condensate (BEC) in a double well potential. In a two-mode Fock-state analysis we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase space information is extracted from the stationary quantum states using the Husimi distribution function. It is shown that the quantum states are localized on the known classical phase space orbits of a nonrigid physical pendulum, and thus the novel phase space characteristics of a nonrigid physical pen…
We propose a method of measuring diffusion of the relative phase between two Bose-Einstein condensates occupying different nuclear or spin hyperfine states coupled by a two-photon transition via an intermediate level. Due to the macroscopic quantum coherence the condensates can be decoupled from the electromagnetic fields. The rate of decoherence and the phase collapse may be determined from the occupation of the intermediate level or the absorption of radiation.
Atom chips provide compact and robust platforms towards practical quantum technologies. A quick and faithful preparation of arbitrary input states for these systems is crucial but represents a very challenging experimental task. This is especially difficult when the dynamical evolution is noisy and unavoidable setup imperfections have to be considered. Here, we experimentally prepare with very high small errors different internal states of a Rubidium Bose-Einstein condensate realized on an atom chip. As a possible application of our scheme, we apply it to improve the sensitivity of an atomic i…
We discuss the properties of two Bose-Einstein condensates in different spin states, represented quantum mechanically by a double Fock state. Individual measurements of the spins of the particles are performed in transverse directions (perpendicular to the spin quantization axis), giving access to the relative phase of the two macroscopically occupied states. Before the first spin measurement, the phase is completely undetermined; after a few measurements, a more and more precise knowledge of its value emerges under the effect of the quantum measurement process. This naturally leads to the usu…
We examine the quantum tunneling process in Bose condensates of two interacting species trapped in a double well configuration. We discover the condition under which particles of different species can tunnel as pairs through the potential barrier between two wells in opposition directions. This novel form of tunneling is due to the interspecies interaction that eliminates the self- trapping effect. The correlated motion of tunneling atoms leads to the generation of quantum entanglement between two macroscopically coherent systems.
Cold-atom interferometry is a powerful tool for high-precision measurements of the quantum properties of atoms, many-body interactions and gravity. Further enhancement of sensitivity and reduction of complexity of these devices are crucial conditions for success of their applications. Here we introduce a multi-path interferometric scheme that offers advances in both these aspects. It uses coherent coupling between Bose-Einstein condensates in different Zeeman states to generate an interferometric signal with sharp fringes. We realise such an interferometer as a compact easy-to-use atom-chip de…
