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Quantum Control of BEC in Optical Lattice

Quan‐Fang Wang

Published Apr 27, 2021• 0 citations
Publisher

Abstract

In this paper, it would be worthwhile to consider the theoretical and computational approach of controlling Bose-Einstein Condensates (BEC). In high spatial dimension (2D/3D) case, the BEC system is controlled under external force in trapped optical lattice at low temperature. Finally, our conclusion is in accordance with the results in physics/chemistry realms.

DOI
10.26434/chemrxiv.14474334.v1

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arXiv:0708.2128•Physical Review A•Jan 2, 2008•36 citations
In this paper, it would be worthwhile to consider the theoretical and computational approach of controlling Bose-Einstein Condensates (BEC). In high spatial dimension (2D/3D) case, the BEC system is controlled under external force in trapped optical lattice at low temperature. Finally, our conclusion is in accordance with the results in physics/chemistry realms.
Quantum control of Bose-Einstein-Condensates (BEC) had been found for one and two dimension cases. Firstly in this paper, we want to control BEC at electro-magnetic field in three dimension optical lattice theoretically. The trapped particles in constructed lattices can be made and controlled by optical pulse, and known as molasses. It is evident that quantum control theory is worked for physical particles in BEC status. It is a survey with system control and quantum particle physics. Future work is to focus on collaborating with real laboratory.
In this work, quantum control of trapped Bose-Einstein-Condensates (BEC) is considered at matter surface. For particles at BEC status, quantum system is described by Gross-Pitaevskii equation, experimental control of BEC is happened at physics field, and achieved at laboratory. At theoretic aspect, control of trapped condensates is not sufficiently investigated at academic level. What we interest is applying control theory to BEC trapped on the surface (metallic, crystal). At optical lattice, particles are trapping by constrained forces at cooling technique, and temporally take the same quantum states, such kind of condensates phenomena had already been surveyed at a variety of areas. The most works are reported on free BEC particles, quite natural question is arising on the surface science: BEC particles created,detected, and placed on a certain chemical surface, control of trapped particles is difference or not? We are curious about optical and mechanical constraints take action together on particles. In the viewpoint of quantum control realm, our purpose is to apply optimal control theory (OCT) to trapped Bose-Einstein-Condensates as they are occurred at surface. In the framework of variational theory at complex Hilbert spaces, prove the existence of quantum optimal control, and characterize optimal control using optimality (Euler-Lagrange) system. Control variables for trapped BEC contain three functions: one is electro-magnetic force; another is external constraint from optical equipment (optical frequency, lattice number); third is quantum mechanics against gravitational force, which making BEC particles stay at surface stationary. Review the literatures, electro-magnetic-optical controls are extremely considered at last couple of years. Gravitational control is rarely considered. Further extension of the work is to do real-time computer-aided BEC control at matter surface. Computational approach for simulation of BEC control at two and three dimensions would be a promise direction.
In this work, quantum control of trapped Bose-Einstein-Condensates (BEC) is considered at matter surface. For particles at BEC status, quantum system is described by Gross-Pitaevskii equation, experimental control of BEC is happened at physics field, and achieved at laboratory. At theoretic aspect, control of trapped condensates is not sufficiently investigated at academic level. What we interest is applying control theory to BEC trapped on the surface (metallic, crystal). At optical lattice, particles are trapping by constrained forces at cooling technique, and temporally take the same quantum states, such kind of condensates phenomena had already been surveyed at a variety of areas. The most works are reported on free BEC particles, quite natural question is arising on the surface science: BEC particles created,detected, and placed on a certain chemical surface, control of trapped particles is difference or not? We are curious about optical and mechanical constraints take action together on particles. In the viewpoint of quantum control realm, our purpose is to apply optimal control theory (OCT) to trapped Bose-Einstein-Condensates as they are occurred at surface. In the framework of variational theory at complex Hilbert spaces, prove the existence of quantum optimal control, and characterize optimal control using optimality (Euler-Lagrange) system. Control variables for trapped BEC contain three functions: one is electro-magnetic force; another is external constraint from optical equipment (optical frequency, lattice number); third is quantum mechanics against gravitational force, which making BEC particles stay at surface stationary. Review the literatures, electro-magnetic-optical controls are extremely considered at last couple of years. Gravitational control is rarely considered. Further extension of the work is to do real-time computer-aided BEC control at matter surface. Computational approach for simulation of BEC control at two and three dimensions would be a promise direction.
Quantum control of Bose-Einstein-Condensates (BEC) had been found for one and two dimension cases. Firstly in this paper, we want to control BEC at electro-magnetic field in three dimension optical lattice theoretically. The trapped particles in constructed lattices can be made and controlled by optical pulse, and known as molasses. It is evident that quantum control theory is worked for physical particles in BEC status. It is a survey with system control and quantum particle physics. Future work is to focus on collaborating with real laboratory.
In the present paper, we analytically and numerically investigate the dynamics of Bose-Einstein condensates (BECs) loaded into deep optical lattices of one dimension (1D), 2D, and 3D. We focus on the self-trapped state and the effect of the lattice dimension. Under the tight-binding approximation, we obtain an analytical criterion for the self-trapped state of BEC using the time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of a BEC cloud is obtained accordingly and verified by directly solving a discrete Gross-Pitaevskii equation numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the optical lattices.