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Macroscopic superposition states in rotating ring lattices

Ana Maria Rey A, Andreas Nunnenkamp B

Published Nov 20, 2012• 5 citations
OpenAlex

Abstract

We investigate the effects of rotation on one-dimensional ultracold bosons confined to optical ring lattices. First, we consider a uniform lattice and show that there exists a critical rotation frequency at which the ground state of a weakly-interacting and integer-filled atomic gas is fragmented into a macroscopic superposition of two states with different circulation. Second, we point out several advantages of slightly non-uniform ring lattices for the generation of such kind of states. Finally, we demonstrate 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.

Related papers

Macroscopic superposition states in rotating ring lattices

Andreas Nunnenkamp, Ana Maria Rey

We investigate the effects of rotation on one-dimensional ultracold bosons confined to optical ring lattices. First, we show that there exists a critical rotation frequency at which the ground state of a weakly interacting and integer-filled atomic gas is fragmented into a macroscopic superposition state with different circulation. Second, we point out several advantages of using slightly non-uniform ring lattices. Finally, we demonstrate 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.

arXiv:0802.4309•Journal of Modern Optics•Nov 10, 2008•3 citations

Generation of macroscopic superposition states in ring superlattices

Andreas Nunnenkamp, Ana María Rey, Keith R. Burnett

Ultracold bosons in rotating ring lattices have previously been shown to form macroscopic superpositions of different quasimomentum states. We demonstrate that the generation of this kind of state using slightly nonuniform ring lattices has several advantages: the energy gap decreases less severely with increasing number of particles, the sensitivity to detunings from the critical rotation frequency is reduced, and the scheme is not limited to commensurate filling. We show that different quasimomentum 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.

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Strong correlations in ultracold atomic gases

Andreas Nunnenkamp

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.

•Jan 1, 2008•0 citations

Entanglement and the Mott transition in a rotating bosonic ring lattice

Ana María Rey, Keith R. Burnett, Indubala I. Satija +1 more

We use second- and fourth-order correlation functions accessible in time-of-flight images to investigate the effects of rotation on one-dimensional ultracold bosons confined to a ring lattice. There exists a critical rotation frequency at which the ground state of a weakly interacting and integer-filled atomic gas is fragmented into a macroscopic superposition of two states with different circulation. The formation of such a quantum superposition (``cat'') state is accompanied by the opening of a gap in the spectrum, and by a sudden rearrangement of the momentum distribution which lowers the threshold of the Mott insulator transition. We show that both the entangled character of the ground state and the enhancement of quantum correlations can be detected in the density-density correlations of the expanding cloud. Our studies demonstrate the usefulness of these correlations for identifying physics in cold atomic systems.

arXiv:cond-mat/0611332•Physical Review A•Jun 18, 2007•39 citations

Strong correlations in quantum vortex nucleation of ultracold atomic gases

Andreas Nunnenkamp, Ana Maria Rey, Keith Burnett

We review some recent developments in the theory of rotating atomic gases. These studies have thrown light on the process of nucleation of vortices in regimes where mean-field methods are inadequate. In our review, we shall describe and compare quantum vortex nucleation of a dilute ultracold bosonic gas trapped in three different configurations: a one-dimensional ring lattice, a one-dimensional ring superlattice and a two-dimensional asymmetric harmonic trap. In all of them, there is a critical rotation frequency, at which the particles in the ground state exhibit strong quantum correlations. However, the entanglement properties vary significantly from case to case. We explain these differences by characterizing the intermediate states that participate in the vortex nucleation process. Finally, we show that noise correlations are sensitive to these differences. These new studies have, therefore, shown how novel quantum states may be produced and probed in future experiments with rotating neutral atom systems.

arXiv:0911.4487•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Mar 10, 2010•7 citations

Strong correlations in quantum vortex nucleation of ultracold atomic gases

Andreas Nunnenkamp, Ana María Rey, Keith R. Burnett

We review some recent developments in the theory of rotating atomic gases. These studies have thrown light on the process of nucleation of vortices in regimes where mean-field methods are inadequate. In our review we shall describe and compare quantum vortex nucleation of a dilute ultracold bosonic gas trapped in three dif-ferent configurations: a one-dimensional ring lattice, a one-dimensional ring super-lattice and a two-dimensional asymmetric harmonic trap. In all of them there is a critical rotation frequency, at which the particles in the ground state exhibit strong quantum correlations. However, the entanglement properties vary significantly from case to case. We explain these differences by characterizing the intermediate states that participate in the vortex nucleation process. Finally, we show that noise corre-lations are sensitive to these differences. These new studies have, therefore, shown how novel quantum states may be produced and probed in future experiments with rotating neutral atom systems.

•Aug 16, 2016•3 citations
We investigate the effects of rotation on one-dimensional ultracold bosons confined to optical ring lattices. First, we consider a uniform lattice and show that there exists a critical rotation frequency at which the ground state of a weakly-interacting and integer-filled atomic gas is fragmented into a macroscopic superposition of two states with different circulation. Second, we point out several advantages of slightly non-uniform ring lattices for the generation of such kind of states. Finally, we demonstrate 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.
We investigate the effects of rotation on one-dimensional ultracold bosons confined to optical ring lattices. First, we show that there exists a critical rotation frequency at which the ground state of a weakly interacting and integer-filled atomic gas is fragmented into a macroscopic superposition state with different circulation. Second, we point out several advantages of using slightly non-uniform ring lattices. Finally, we demonstrate 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.
Ultracold bosons in rotating ring lattices have previously been shown to form macroscopic superpositions of different quasimomentum states. We demonstrate that the generation of this kind of state using slightly nonuniform ring lattices has several advantages: the energy gap decreases less severely with increasing number of particles, the sensitivity to detunings from the critical rotation frequency is reduced, and the scheme is not limited to commensurate filling. We show that different quasimomentum 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.
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 use second- and fourth-order correlation functions accessible in time-of-flight images to investigate the effects of rotation on one-dimensional ultracold bosons confined to a ring lattice. There exists a critical rotation frequency at which the ground state of a weakly interacting and integer-filled atomic gas is fragmented into a macroscopic superposition of two states with different circulation. The formation of such a quantum superposition (``cat'') state is accompanied by the opening of a gap in the spectrum, and by a sudden rearrangement of the momentum distribution which lowers the threshold of the Mott insulator transition. We show that both the entangled character of the ground state and the enhancement of quantum correlations can be detected in the density-density correlations of the expanding cloud. Our studies demonstrate the usefulness of these correlations for identifying physics in cold atomic systems.
We review some recent developments in the theory of rotating atomic gases. These studies have thrown light on the process of nucleation of vortices in regimes where mean-field methods are inadequate. In our review, we shall describe and compare quantum vortex nucleation of a dilute ultracold bosonic gas trapped in three different configurations: a one-dimensional ring lattice, a one-dimensional ring superlattice and a two-dimensional asymmetric harmonic trap. In all of them, there is a critical rotation frequency, at which the particles in the ground state exhibit strong quantum correlations. However, the entanglement properties vary significantly from case to case. We explain these differences by characterizing the intermediate states that participate in the vortex nucleation process. Finally, we show that noise correlations are sensitive to these differences. These new studies have, therefore, shown how novel quantum states may be produced and probed in future experiments with rotating neutral atom systems.
We review some recent developments in the theory of rotating atomic gases. These studies have thrown light on the process of nucleation of vortices in regimes where mean-field methods are inadequate. In our review we shall describe and compare quantum vortex nucleation of a dilute ultracold bosonic gas trapped in three dif-ferent configurations: a one-dimensional ring lattice, a one-dimensional ring super-lattice and a two-dimensional asymmetric harmonic trap. In all of them there is a critical rotation frequency, at which the particles in the ground state exhibit strong quantum correlations. However, the entanglement properties vary significantly from case to case. We explain these differences by characterizing the intermediate states that participate in the vortex nucleation process. Finally, we show that noise corre-lations are sensitive to these differences. These new studies have, therefore, shown how novel quantum states may be produced and probed in future experiments with rotating neutral atom systems.