arXiv:0906.1894 · International Journal of Modern Physics B

TWO-PHOTON NONLINEAR SPECTROSCOPY OF PERIODICALLY TRAPPED ULTRACOLD ATOMS IN A CAVITY

Tarun Kumar, Aranya B. Bhattacherjee, ManMohan

Published Apr 6, 2011• 2 citations

Abstract

We study the transmission spectra of a Bose Einstein condensate (BEC) confined in an optical lattice interacting with two modes of a cavity via nonlinear two-photon transition. In particular, we show that the one-photon and two-photon cavity transmission spectra of a BEC are different. We found that when the BEC is in the Mott state, the usual normal mode splitting present in the one-photon transition is missing in the two-photon interaction. When the BEC is in the superfluid state, the transmission spectrum shows the usual multiple lorentzian structure. However the separation between the lorentzians for the two-photon case is much larger than that for the one-photon case. This study could form the basis for nondestructive high resolution Rydberg spectroscopy of ultracold atoms or two-photon spectroscopy of a gas of ultracold atomic hydrogen.

DOI: 10.1142/s0217979211100631

Related papers

Quantum phases of bosonic atoms with two levels coupled by a cavity field in an optical lattice

Hashem Zoubi, Helmut Ritsch

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.

arXiv:0902.2638Physical Review ANov 11, 200913 citations

Study of Transmission Spectrum of an Optical Cavity Loaded with Ultracold Atoms

Jasleen Lugani, Sankalpa Ghosh, Krishna Thyagarajan

We analyze transmission spectra of an optical cavity loaded with ultracold atoms in optical lattices. We primarily consider how transmission spectrum changes for a Mott insulator to superfluid, and density wave to supersolid phase transition.

Frontiers in OpticsJan 1, 20120 citations

Probing superfluidity of periodically trapped ultracold atoms in a cavity by transmission spectroscopy

Aranya B. Bhattacherjee, Tarun Kumar, Man Mohan

Abstract We study a system of periodic Bose-condensed atoms coupled to cavity photons using the input-output formalism of [14]. We show for the first time that the cavity will either act as a through-pass Lorentzian filter when the superfluid fraction of the condensate is minimum, or completely reflect the input field when the superfluid fraction is maximum. We show that by monitoring the ratio between the transmitted field and the reflected field, one can estimate the superfluid fraction.

arXiv:0905.0817Open PhysicsDec 1, 20093 citations

QUANTUM DEGENERATE ATOMIC GASES IN OPTICAL CAVITIES

Wenzhou Chen

This dissertation contains a study of ultracold atoms in optical cavities. We particularly focus on two aspects of the coupled atom-cavity systems. In the first aspect, we implement the quantum nature of the light field to probe the quantum state of the atoms. This is interesting due to the nondestructive nature of the characterization of many-body atomic states. In the second aspect we study the cavity optomechanics that investigates the coupling of mechanical and optical degrees of freedom via radiation pressure. The optomechanical cavity provides an interesting nonlinear system to study the coupling between atoms and the intracavity field.In the context of cavity quantum electrodynamics we study the reflection of two counter-propagating modes of the light field in a high-Q ring cavity by ultracold atoms either in the Mott insulator state or in the superfluid state of an optical lattice. We find that the dynamics of the reflected light strongly depends on both the lattice spacing and the state of the matter-wave field. By using the Monte Carlo wave-function method to account for the cavity damping we also determine the two-time correlation function and the time-dependent physical spectrum of theretroreflected field. We find that the light field and the atoms become entangled if the latter are in a superfluid state. We also analyze quantitatively the entanglement between the atoms and the light.In cavity optomechanics the mechanical effect can either comes from a vibrating macroscopic oscillator or a collective density excitation of a Bose-Einstein condensate. First we use a Fabry-Perot-type cavity to study the opto-mechanically-induced bistable quantum phase transitions between superfluid and a Mott insulator states of an ultracold bosonic gases trapped inside the cavity. Secondly, we study the symmetricand antisymmetric collective density side modes of the BEC which results from the optomechanical effects of the light fields in a ring cavity.

Jan 1, 20100 citations

Multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate in a cavity

Yuxiang Liu, Pei-Sen He, Sheng-Chang Li

Ramsey interferometry as one of the most important high-precision measurement methods has prospects for inferring various properties of ultracold atoms and molecules. We investigate the multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate (BEC) in an optical cavity. Compared with the standard two-pulse Ramsey scheme, our multi-pulse Ramsey proposal greatly relaxes the requirements for both intensity and width of the pulses, allowing the interferometry to be achieved using weak and narrow pulses. When the pumping pulses characterizing the coupling between the cavity field and the atomic BEC are applied to the zero background field, we demonstrate the atomic Ramsey fringes in the time domain for different pulse numbers and different pulse widths. We find that although the multi-pulse Ramsey fringes are no longer sensitive to cavity-pump detuning, they can still record the information of the interaction between coherent atoms. We obtain the fundamental frequency of the multi-pulse Ramsey fringes analytically and find that it is proportional to the number of pulses. Particularly, it is shown that the minimum of the fundamental frequency is exactly the critical point of the phase transition of the system. For a nonzero background field, the results indicate that a nondestructive observation of atomic Ramsey fringes by cavity transmission spectroscopy is feasible. Our findings provide insights for improving the accuracy of Ramsey interferometry and for using interferometry to observe phase transitions.

Journal of the Optical Society of America BApr 4, 20241 citation

Light propagation in ultracold atomic gases

Stefan Rist

In the present thesis we study several schemes where the detection of the emitted light from an atomic ensemble gives information about the state of the atoms. In chapter 1 we review the basic theory for the light matter interaction in second quantized form. In chapter 2 we show how conservative potentials for the atoms, such as dispersive optical lattices, can be realized experimentally due to the dispersive interaction with a far detuned laser We then review some basic properties of the physics of a particle in a periodic potential. We show that the ground state and the lowest lying excitations of a Bose-Einstein condensate in a dispersive optical lattice can be described by the Bose-Hubbard Hamiltonian. In chapter 3 we study the photonic bandstructure of a chain of fixed pointlike atoms in a biperiodic configuration. We calculate the photonic spectra and the probe transmission if the atoms are in free space and inside a standing wave optical resonator. In chapter 4 we consider light scattering from ultracold atoms in an optical lattice where we calculate the photonic scattering cross section as a function of energy and direction of emission along the Mott-insulator-superfluid phase transition. We take into account the finite tunneling rate for the atoms, when evaluating the scattering cross section of the photons and the effect of photon recoil onto the atoms. In chapter 5 we consider a gas of ultracold atoms trapped at two spatially separated regions in space. Using a two Raman lasers to couple atoms out of the systems we show that it is possible to measure the mean value of the atomic field operator of the two systems by measuring the scattered light intensity of one of the Raman lasers. We show how this setup might be used to measure the temperature of a Bose-Einstein condensate and to monitor the superfluid to Mott-insulator phase transition for a gas of ultracold atoms in an optical lattice.

Jan 1, 20100 citations