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Optics Express

Detecting quantum coherence of Bose gases in optical lattices by scattering light intensity in cavity

Xiaoji Zhou, Xu Xu, Lan Yin, W. M. Liu, Xuzong Chen

Published Jul 9, 2010• 7 citations
Publisher

Abstract

We propose a new method of detecting quantum coherence of a Bose gas trapped in a one-dimensional optical lattice by measuring the light intensity from Raman scattering in cavity. After pump and displacement process, the intensity or amplitude of scattering light is different for different quantum states of a Bose gas, such as superfluid and Mott-Insulator states. This method can also be useful to detect quantum states of atoms with two components in an optical lattice.

DOI
10.1364/oe.18.015664

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We propose a new method of detecting quantum coherence of a Bose gas trapped in a one-dimensional optical lattice by measuring the light intensity from Raman scattering in cavity. After pump and displacement process, the intensity or amplitude of scattering light is different for different quantum states of a Bose gas, such as superfluid and Mott-Insulator states. This method can also be useful to detect quantum states of atoms with two components in an optical lattice.
We consider collective light scattering from ultracold atoms trapped in a deep optical lattice. Different atomic quantum states were shown to exhibit qualitatively different light scattering. This suggests a novel nondestructive method to probe atomic quantum statistics and characterize quantum phase transitions, e.g., between Mott insulator and superfluid states. The method is based on measurements of light fields only, in contrast to the standard methods based on matter-field interference, which destroys the system.
We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without optical access to a single site) and pair correlations between different sites. As a striking example we consider scattering from transversally illuminated atoms into an optical cavity mode. For the Mott-insulator state, similar to classical diffraction, the number of photons scattered into a cavity is zero due to destructive interference, while for the superfluid state it is nonzero and proportional to the number of atoms. Moreover, we demonstrate that light scattering into a standing-wave cavity has a nontrivial angle dependence, including the appearance of narrow features at angles, where classical diffraction predicts zero. The measurement procedure corresponds to the quantum nondemolition measurement of various atomic variables by observing light.
An optical lattice is a periodic potential for atoms, created using a standing wave pattern of light. Due to the interaction between the light and the atoms, the atoms are attracted to either the nodes or the anti-nodes of the standing wave, depending on the exact wave lenght of the light. This means that if such a lattice is loaded with a sufficiently high number of ultracold atoms, a periodic array of atoms is obtained, we an interatomic distance of a few tenths of a micrometer. In order to obtain such a high number of cold atoms, one first has to create a so-called Bose-Einstein condensate. When an optical lattice is loaded from a Bose-Einstein condensate, it is possible to create a system in which every atom is in the lowest band of the lattice and there is on average one atom in each lattice site. Because the lattice potential is created with laser light, the depth of the lattice can easily be tuned by changing the intensity of the laser. When the intensity of the laser light is low, the atoms can tunnel from one site to the next. Due to this tunneling, the gas of atoms in the lattice will remain superfluid. However, if the intensity of the laser light is increased to above a certain critical value, a quantum phase transition occurs to a so-called Mott insulator. In this state, the atoms can no longer tunnel due to the fact that the on-site interaction between atoms becomes more important then the tunneling probability. In this PhD thesis, a description is given of the experimental setup that is being constructed in our group to create these systems in our lab. Also, a theoretical description is given of these systems and several important quantities our derived, such as the gap of the Mott-insulating state. Furthermore, an experiment is proposed that can be used to accurately measure this gap.
Bose–Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ∼ 13.7 E r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.
For the one-dimensional Bose-Hubbard theoretical model of condensed matter,the quantum phase transition process of the superfluid-Mott insulation state in the one-dimensional Bose-Hubbard model is realized by continuously changing the depth of the optical lattice well and preparing the temperature of the quantum gas.Through the ultra-cold atomic Time of Flight(TOF) imaging method,the interference pattern of the momentum space of the quantum gas in the diffusion process is analyzed,and the change data of the superfluid component and the Mott insulation state component in the quantum phase transition process are obtained.Experimental results show that the quantum gas in the optical lattice can simulate the one-dimensional Bose-Hubbard theoretical model.