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Robust Mesoscopic Superposition of Ultracold Atoms

D. W. Hallwood, T. Ernst, Joachim Brand

Published Jul 23, 2010• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
Quantum correlations are correlations that arise from a unique feature in quantum mechanics: quantum superposition. The most famous example of quantum superposition is the Schrodinger’s cat state, where a cat is in a state of neither dead nor alive before an observer determines the cat’s status. This is not what we expect. Nevertheless, quantum superposition and correlations are routinely created in the laboratories with microscopic systems involving atoms and light particles. Can this counterintuitive notion be realised in the macroscopic world? This thesis investigates this question by devising criteria that certify the existence of quantum correlations in mesoscopic/macroscopic systems. Powerful mathematical tools are used to simulate two quantum protocols in a mesoscopic system which have applications in quantum communication and computation.
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 NNN 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 superposition for this system, which agrees well with direct diagonalisation of the Hamiltonian for relatively small numbers of atoms. We show that for macroscopic superpositions to be realised there are essentially three straightforward requirements, other than an absence of decoherence, which become harder to achieve as the system size increases. Firstly, the energies of the two distinct superfluid states must be sufficiently close. Secondly, coupling between the two states must be sufficiently strong, and thirdly, other states must be well separated from those participating in the superposition.
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 superposition for this system, which agrees well with direct diagonalization of the Hamiltonian for relatively small numbers of atoms. We show that for macroscopic superpositions to be realized there are essentially three straightforward requirements, other than an absence of decoherence, which become harder to achieve as the system size increases. Firstly, the energies of the two distinct superfluid states must be sufficiently close. Secondly, coupling between the two states must be sufficiently strong, and thirdly, other states must be well separated from those participating in the superposition.
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 (BECs) 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 simplicity of the model has allowed us to study macroscopic superpositions at an atomic level for different variables. Here, we concentrate on the tunnelling strength between the potentials. Further investigation remains important, because it could lead us to making an ultra-precise quantum-limited gyroscope.