We propose a scheme to create coherent superpositions of annular flow of strongly interacting bosonic atoms in a one-dimensional ring trap. The nonrotating 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 than in schemes relying on weak interactions, thus making particle numbers of hundreds or thousands feasible. Coherent oscillations induced by time variation of parameters may serve as a ``smoking gun'' signature for detecting superposition states.
We propose a scheme to create coherent superpositions of annular flow of strongly interacting bosonic atoms in a one-dimensional ring trap. The nonrotating 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 than in schemes relying on weak interactions, thus making particle numbers of hundreds or thousands feasible. Coherent oscillations induced by time variation of parameters may serve as a ``smoking gun'' signature for detecting superposition states.
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 nonideal 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-Girardeau, regime, which is also the most robust at finite temperature. NOON-type superpositions of weakly interacting atoms are most easily created by adiabatically decreasing the interaction strength by means of a Feshbach resonance. The quantum dynamics of small numbers of particles is simulated and the size of the superpositions is calculated based on their ability to make precision measurements. The experimental creation of strongly correlated and NOON-type superpositions with about 100 atoms seems feasible in the near future.
Quantum superpositions of macroscopically distinct states, as in Schrodinger’s example of a dead and alive cat, are important for our understanding of quantum mechanics [1] and carry great promise for enhanced precision measurement techniques [2]. Due to their inherent fragility, the maximally entangled “NOON” states engineered in optics and spin systems for ultra-precise spectroscopy have been limited to 10 particles [3]. The related mesoscopic superpositions of flux states consisting of 10 Cooper pairs observed in superconducting rings [4, 5] have proven more robust but their microscopic nature is debated [6–9]. Binary superpositions with multiple ultra-cold atoms have not yet been seen and existing proposals suffer severe limitations due to decoherence [10] and the unfavorable scaling of precision and time scales needed to produce these states [11, 12]. In this paper we show how robust superpositions of mesoscopic flow in a ring trap can be made with stronglycorrelated ultra-cold atoms under one-dimensional confinement. We present a microscopic model that explains how flow states become robust to single-particle loss due to strong correlations between atoms. The attainable spectroscopic energy separation scales linearly with particle number and thus does not limit the system size. Our results introduce a new type of binary superposition state that involves mesoscopically distinct and strongly correlated quantum states.
We consider a strongly interacting quasi-one-dimensional Bose gas on a tight ring trap subjected to a localized barrier potential. We explore the possibility of forming a macroscopic superposition of a rotating and a nonrotating state under nonequilibrium conditions, achieved by a sudden quench of the barrier velocity. Using an exact solution for the dynamical evolution in the impenetrable-boson (Tonks-Girardeau) limit, we find an expression for the many-body wave function corresponding to a superposition state. The superposition is formed when the barrier velocity is tuned close to multiples of an integer or half-integer number of Coriolis flux quanta. As a consequence of the strong interactions, we find that (i) the state of the system can be mapped onto a macroscopic superposition of two Fermi spheres rather than two macroscopically occupied single-particle states as in a weakly interacting gas, and (ii) the barrier velocity should be larger than the sound velocity to better discriminate the two components of the superposition.
In this thesis we investigate strongly-correlated states of ultracold bosonic atoms in rotating ring lattices and arrays of double-well potentials. In the first part of the thesis, we study the tunneling dynamics of ultracold bosons in double-well potentials. In the non-interacting limit single-particle transitions dominate, while in the interaction-dominated regime correlated tunneling of all particles prevails. At intermediate times of the many-particle flopping process correlated states occur, but the timescales of these processes increase dramatically with the number of particles. Using an array of double-well potentials, a large number of such few-particle superposition states can be produced in parallel. In the second part of the thesis, we study the effects of rotation on ultracold bosons confined to one-dimensional ring lattices. We find that at commensurate filling there exists a critical rotation frequency, at which the ground state of the weakly-interacting gas is fragmented into a macroscopic superposition of different quasi-momentum states. We demonstrate that the generation of such superposition states using slightly non-uniform ring lattices has several practical advantages. Moreover, we show that different quasi-momentum states can be distinguished in time-of-flight absorption imaging and propose to probe correlations via the many-body oscillations induced by a sudden change in the rotation frequency. Finally, we compare these macroscopic superposition states to those occurring in superconducting quantum interference devices. In the third part of the thesis, we demonstrate the creation of entangled states with ultracold bosonic atoms by dynamical manipulation of the shape of the lattice potential. To this end, we consider an optical superlattice that allows both the splitting of each site into a double-well potential and the variation of the height of the potential barrier between the sites. We show how to use this array of double-well potentials to perform entangling operations between neighboring qubits encoded on the Zeeman levels of the atoms. As one possible application, we present a method of realizing a resource state for measurement-based quantum computation via Bell-pair measurements. In the final part of the thesis, we study ultracold bosons on a two-dimensional square lattice in the presence of an effective magnetic field and point out a couple of features this system has in common with ultracold bosons in one-dimensional rotating ring lattices.
We study Josephson oscillations of two strongly correlated one-dimensional bosonic clouds separated by a localized barrier. Using a quantum-Langevin approach and the exact Tonks-Girardeau solution in the impenetrable-boson limit, we determine the dynamical evolution of the particle-number imbalance, displaying an effective damping of the Josephson oscillations which depends on barrier height, interaction strength, and temperature. We show that the damping originates from the quantum and thermal fluctuations intrinsically present in the strongly correlated gas. Because of the density-phase duality of the model, the same results apply to particle-current oscillations in a one-dimensional ring where a weak barrier couples different angular momentum states.
We theoretically investigate the properties of ultracold dipolar atoms in radially coupled, concentric annular traps created by a potential barrier. The nonrotating ground-state phases are investigated across the superfluid-supersolid phase transition, revealing a particle imbalance between the two rings and a preferential density modulation in the outer ring in the absence of rotation. Near the phase transition on the superfluid side, applying rotation can induce density modulations in either ring, depending on the angular momentum and barrier strength. For low angular momentum, such rotation-induced density modulation forms in the outer ring, while for high angular momentum and weak barriers, it emerges in the inner ring. Rotation can lead to persistent currents and the nucleation of a vortex residing either at the center (central vortex) or at the ring junction (Josephson vortex). Josephson vortices can also form at the junctions of the localized density sites induced by rotation in the inner ring, a behavior that is unique to our system. By switching off the trap and allowing the system to expand, distinct interference patterns emerge, which can be analyzed to identify and distinguish between various vortex configurations, and thus can be observed in current state-of-the-art experiments.