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arXiv:1403.7369 · Journal of Physics B Atomic Molecular and Optical Physics

Identifying insulating states of ultra cold atoms with cavity transmission spectrum

Jasleen Lugani, K Thyagarajan, Sankalpa Ghosh

Published Jan 29, 2014• 0 citations
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Abstract

In this paper, we consider the transmission characteristics of an optical cavity loaded with ultra cold atoms in a one dimensional optical lattice at absolute zero temperature. In particular, we consider the situation when the many body quantum state of the ultra cold atoms is an insulating state with fixed number of atoms at each site, which can be either density wave (DW) or Mott insulator (MI) phase, each showing different type of discrete lattice translational symmetry. We provide a general framework of understanding the transmission spectrum from a single and two cavities/modes loaded with such insulating phases. Further, we also discuss how such a transmission spectrum changes when these insulating phases make a cross over to the superfluid (SF) phase with the changing depth of the optical lattice potential.

DOI
10.1088/0953-4075/47/4/045301

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In this paper, we consider the transmission characteristics of an optical cavity loaded with ultra cold atoms in a one dimensional optical lattice at absolute zero temperature. In particular, we consider the situation when the many body quantum state of the ultra cold atoms is an insulating state with fixed number of atoms at each site, which can be either density wave (DW) or Mott insulator (MI) phase, each showing different type of discrete lattice translational symmetry. We provide a general framework of understanding the transmission spectrum from a single and two cavities/modes loaded with such insulating phases. Further, we also discuss how such a transmission spectrum changes when these insulating phases make a cross over to the superfluid (SF) phase with the changing depth of the optical lattice potential.
Light transmission or diffraction from different quantum phases of cold atoms in an optical lattice has recently come up as a useful tool to probe such ultracold atomic systems. The periodic nature of the optical lattice potential closely resembles the structure of a diffraction grating in real space but is loaded with a strongly correlated quantum many-body state which interacts with the incident electromagnetic wave, a feature that controls the nature of light transmission or dispersion through such quantum media. In this paper we show that, as one varies the relative angle between the cavity mode and the optical lattice, the peak of the transmission spectrum through such cavities also changes, which reflects the statistical distribution of the atoms in the illuminated sites. Consequently, the angle-resolved transmission spectrum of such quantum diffraction gratings can provide a plethora of information about the Fock-space structure of the many-body quantum state of ultracold atoms in such an optical cavity that can be explored in current state-of-the-art experiments.
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.
We study the quantum phase transition between superfluid and Mott-insulator states for ultracold bosons with two internal states forming two bands of an optical lattice. The two atomic states are resonantly coupled by a coherent field enclosed in a single cavity mode, which mediates transitions between the two bosonic particle modes via absorption or emission of cavity photons. As nonlocal atomic coherence can build up via photon assisted tunneling, this coupling shifts the transition to the Mott-insulator phase toward deeper lattice potentials and stronger on-site interaction. Varying the intra and interband on-site interactions leads to several different atomic phase configurations. There are even parameter regions, where a mean-field approach predicts concurrence of a Mott-insulator state in one band and a superfluid in the other band.
Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. The theory is based on a change of variables in which the boson coherent state amplitude is replaced by an effective potential which promotes phase coherence between different number states on each lattice site. It is illustrated here by applying it to uniform and fully frustrated lattice cases but is simple enough that it can be applied to spatially inhomogeneous lattice systems.
We discuss the superfluid (SF) to Mott-insulator transition of cold atoms in optical lattices recently observed by Greiner et al (2002 Nature 415 39). The fundamental properties of both phases and their experimental signatures are discussed carefully, including the limitations of the standard Gutzwiller approximation. It is shown that in a one-dimensional dilute Bose-gas with a strong transverse confinement (Tonks-gas), even an arbitrary weak optical lattice is able to induce a Mott-like state with crystalline order, provided the dimensionless interaction parameter is larger than a critical value of order one. The SF–insulator transition of the Bose–Hubbard model in this case continuously evolves into a transition of the commensurate–incommensurate type with decreasing strength of the external optical lattice.