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arXiv:1802.02407 · New Journal of Physics

Management of the correlations of UltracoldBosons in triple wells

Sunayana Dutta, Marios C Tsatsos, Saurabh Basu, Axel U. J. Lode

Published May 1, 2019• 17 citations
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Abstract

Abstract Ultracold interacting atoms are an excellent tool to study correlation functions of many-body systems that are generally eluding detection and manipulation. Herein, we investigate the ground state of bosons in a tilted triple-well potential and characterize the many-body state by the eigenvalues of its reduced one-body density matrix and Glauber correlation functions. We unveil how the interplay between the interaction strength and the tilt can be used to control the number of correlated wells as well as the fragmentation, i.e. the number of macroscopic eigenvalues of the reduced one-body density matrix.

DOI
10.1088/1367-2630/ab117d

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•Jan 1, 2008•0 citations
Abstract Ultracold interacting atoms are an excellent tool to study correlation functions of many-body systems that are generally eluding detection and manipulation. Herein, we investigate the ground state of bosons in a tilted triple-well potential and characterize the many-body state by the eigenvalues of its reduced one-body density matrix and Glauber correlation functions. We unveil how the interplay between the interaction strength and the tilt can be used to control the number of correlated wells as well as the fragmentation, i.e. the number of macroscopic eigenvalues of the reduced one-body density matrix.
Strongly interacting finite ensembles of dipolar bosons in commensurately filled one-dimensional optical lattices exhibit diverse quantum phases that are rich in physics. As the strength of the long-range boson–boson interaction increases, the system transitions across different phases: from a superfluid, through a Mott-insulator and a Tonks–Girardeau gas to a crystal state. The signature of these phases and their transitions can be unequivocally identified by an experimentally detectable order parameter, recently described in Phys. Rev. A 98 235301 (2018 [ 33 ]). Herein, we calculate the momentum distributions and the normalized Glauber correlation functions of dipolar bosons in a one-dimensional optical lattice in order to characterize all their phases. To understand the behavior of the correlations across the phase transitions, we first investigate the eigenfunctions and eigenvalues of the one-body reduced density matrix as a function of the dipolar interaction strength. We then analyze the real- and momentum-space Glauber correlation functions, thereby gaining a spatially and momentum-resolved insight into the coherence properties of these quantum phases. We find an intriguing structure of non-local correlations that, independently of other observables, reveal the phase transitions of the system. In particular, spatial localization and momentum delocalization accompany the formation of correlated islands in the density as interactions become stronger. Our study showcases that precise control of intersite correlations is possible through the manipulation of the depth of the lattice, while intrasite correlations can be influenced by changing the dipolar interaction strength.
We study the correlation properties of the ground states of few ultracold bosons, trapped in double wells of varying barrier height in one dimension. Extending previous results on the signature of the transition from a Bose-condensed state via fragmentation to the hard-core limit, we provide a deeper understanding of that transition by relating it to the loss of coherence in the one-body density matrix and to the emerging long-range tail in the momentum spectrum. These are accounted for in detail by discussing the natural orbitals and their occupations. Our discussion is complemented by an analysis of the two-body correlation function.
In this work we study the properties of interacting bosons in a tilted triple well optical lattice potential. A tilted optical lattice is possible to create in an experiment with charged bosons in presence of an electric field. The ground state energy, occupation densities in each well and first order correlation function of occupation densities as a function of the tilt parameter for N = 90 bosons using recently developed Multiconfigurational time-dependent Hartree method for bosons (MCTDHB) are studied. The ground state energy falls off with the tilt parameter for a given value of the barrier height and interparticle interaction. Also the tilt parameter is observed to restrict the fragmentation of the occupation densities in each well and thus promote condensation. Further the correlation between the bosons in different wells enhances with the tilt parameter and at large values the bosons in the first and the third wells are correlated apart from the correlation among the bosons in the same well, while the occupancy in the middle one seems to be uncorrelated with the other two. Such correlation between different wells is not observed in absence of the tilt effect for the same barrier height of the potential and interparticle interaction strength.
We investigate the transition of a quasi-one-dimensional few-boson system from a weakly correlated to a fragmented and finally a fermionized ground state. Our numerically exact analysis, based on a multiconfigurational method, explores the interplay between different shapes of external and interparticle forces. Specifically, we demonstrate that the addition of a central barrier to an otherwise harmonic trap may support the system's fragmentation, with a symmetry-induced distinction between even and odd atom numbers. Moreover, the impact of inhomogeneous interactions is studied, where the effective coupling strength is spatially modulated. It is laid out how the ground state can be displaced in a controlled way depending on the trap and the degree of modulation. We present the one- and two-body densities and, beyond that, highlight the role of correlations on the basis of the natural occupations.
The N-body problem in a tilted double well requires new features for macroscopic quantum superposition in ultracold atoms. In particular, one needs to go beyond the single-particle ground state in each well. We provide explicit criteria for when two energy levels are needed to describe the state space. For typical experimental parameters, two levels are indeed required for the creation of macroscopic superposition states. Furthermore, we show that a small tilt causes the collapse of such states. However, partial macroscopic superposition states reappear when the tilt can be compensated by atom-atom interactions.
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.