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arXiv:0803.2265 · Physical Review A

Macroscopic superpositions of phase states with Bose-Einstein condensates

Francesco Piazza, Luca Pezzè, Augusto Smerzi

Published Nov 5, 2008• 33 citations
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Abstract

Quantum superpositions of macroscopically distinguishable states having distinct phases can be created with a Bose-Einstein condensate trapped in a periodic potential. The experimental signature is contained in the phase distribution of the interference patterns obtained after releasing the traps. Moreover, in the double-well case, this distribution exhibits a dramatic dependence on the parity of the total number of atoms. We finally show that, for single-well occupations up to a few hundred atoms, the macroscopic quantum superposition can be robust enough against decoherence to be experimentally revealable within current technology.

DOI
10.1103/physreva.78.051601

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Quantum superpositions of macroscopically distinguishable states having distinct phases can be created with a Bose-Einstein condensate trapped in a periodic potential. The experimental signature is contained in the phase distribution of the interference patterns obtained after releasing the traps. Moreover, in the double-well case, this distribution exhibits a dramatic dependence on the parity of the total number of atoms. We finally show that, for single-well occupations up to a few hundred atoms, the macroscopic quantum superposition can be robust enough against decoherence to be experimentally revealable within current technology.
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 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.
This thesis considers measurements that could be used to verify the existence of a coherent superposition, using the specific example of a superposition of a Bose-Einstein condensate in a double-well. There is significant interest in superposition states in atomic condensates, due to the possibility of large numbers of atoms being involved in the superposition, and while various experimental proposals exist for generating such states none have yet been successfully verified in this system. We use a number-state description of the condensate in a double well, which is a number-conserving approach with basis states specifying the number of atoms in each well. This allows us to consider 'NOON`-type states, i.e. a superposition of the 'N,0' state of all atoms localized in the left well and the '0,N' state where all N atoms are localized in the right hand well. MATLAB is used to solve for the ground state, dynamics, and measurement expectation values for the double-well condensate in this basis. We consider measurements that would distinguish this coherent superposition from a statistical mixture of the same states. Such a suitable measurement is the parity of the atoms in one well, after a Ramsey-type interference experiment has been performed. We have found that unambiguously distinguishing even a perfect 'NOON' state from a statistical mixture using standard detection methods will present experimental difficulties. We find that interactions between condensate atoms degrade the visibility of the parity oscillations, and we also consider the effects of detector inefficiency on these parity measurements. We suggest that a 'NOON'-type superposition state in the double-well system could be generated in a reasonable time frame by making use of a Feshbach resonance to tune the inter-atomic interactions from repulsive to negative. We find that even with imperfect superpositions, parity measurements retain their frequency dependence, which is the signature of NOON-type coherence.
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.
We provide an experimentally viable 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 appropriately phase engineered with specific phase differences between the neighbouring wells, to a macroscopic superposition state with controllable entanglement – as for example the multiple well generalization of double well NOON states. We demonstrate, through numerical simulations, the creation of entangled states of small numbers of particles in three and four wells and then explore the creation of entangled states where there are larger numbers of particles or a larger number of wells. In the four well case we study a novel, initially unexpected, type of entanglement produced as the particle numbers, or interaction strengths, increase.
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.