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arXiv:quant-ph/0605059 · Physical Review A

Creation of macroscopic superpositions of flow states with Bose-Einstein condensates

Jacob Dunningham, D. W. Hallwood

Published Aug 2, 2006• 20 citations
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Abstract

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 within the reach of current experiments. Furthermore, the relative difficulty of creating superpositions scales favorably with the size of the state. 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 angular momentum.

DOI
10.1103/physreva.74.023601

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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 within the reach of current experiments. Furthermore, the relative difficulty of creating superpositions scales favorably with the size of the state. 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 angular momentum.
We give a theoretical analysis of the experimental scheme for creating macroscopic superpositions of different superfluid flow states with Bose-Einstein condensates trapped in an optical lattice [J. Dunningham et al., Phys. Rev. A 74, 023601 (2006)]. It is shown that a class of macroscopic superposition states can be created for an arbitrary number of particles by dynamical evolution with a properly prepared initial state. When the number of particles is a multiple of 3, such states are exactly reduced to macroscopic superpositions of different superfluid flow states.
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.
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 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 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.
Macroscopic superposition states enable fundamental tests of quantum mechanics and hold a huge potential in metrology, sensing, and other quantum technologies. We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a spin-1 Bose-Einstein condensate. Measuring the number of particles in one mode prepares with large probability highly entangled macroscopic superposition states in the two remaining modes. The macroscopic superposition states are heralded by the measurement outcome. Our protocol is robust under realistic conditions in current experiments, including finite adiabaticity, particle loss, and measurement uncertainty.