Cavity-Enhanced Light Scattering in Optical Lattices to Probe Atomic Quantum Statistics

Abstract

Different quantum states of atoms in optical lattices can be nondestructively monitored by offresonant collective light scattering into a cavity. Angle resolved measurements of photon number and variance give information about atom-number fluctuations and pair correlations without single-site access. Observation at angles of diffraction minima provides information on quantum fluctuations insensitive to classical noise. For transverse probing, no photon is scattered into a cavity from a Mott insulator phase, while the photon number is proportional to the atom number for a superfluid. While mean-field approaches describe only the average atomic density, the main goal is to study quantum properties of these gases. They are most prominent in lattices, where one has phase transitions between states of similar density but radically different quantum fluctuations.Standard methods to measure quantum properties are based on matter-wave interference of atoms released from a trap [2] destroying the system. "Bragg spectroscopy" using stimulated matter-wave scattering by laser pulses proved successful [3, 4] but destructive. Alternative less destructive methods observing scattered light were proposed mainly for homogeneous Bose-Einstein condensates (BEC) [5,6,7,8], but not yet implemented.Here we show that specifically for periodic lattices, light scattering can help to overcome experimental difficulties. In contrast to homogeneous BECs, scattering from a lattice allows to determine local and nonlocal correlations without single-atom optical access using the suppression of strong classical scattering at Bragg minima and monitoring much richer angular distributions. This looks extremely useful for studying phase transitions between, e.g., Mott insulator (MI) and superfluid (SF) states, without destruction, since various quantum phases show even qualitatively distinct scattering.Joining two fields, cavity quantum electrodynamics (QED) and ultracold gases, will enable new investigations of both light and matter at ultimate quantum levels, which only recently became experimentally possible [9].Our model is based on nonresonant interaction, not relying on a particle level structure. Thus it also applies to molecular physics, where new quantum phases were obtained [10]. It can be also applied for semiconductors [11], as, e.g., were used for BEC of exciton-polaritons [12].Model. We consider N two-level atoms in an optical lattice with M sites. A region of K ≤ M sites is illuminated by probe light which is scattered into another mode (cf. Fig. 1). Although, each mode could be a freely propagating field, we will consider cavity modes whose geometries (i.e. axis directions or wavelengths) can be varied. A related manybody Hamiltonian is given bywhere a 0 (a 1 ) are the annihilation operators of the probe (scattered) light with the frequencies ω 0,1 , wave vectors k 0,1 , and mode functions u 0,1 (r); Ψ(r) is the atom-field operator. In the effective single-atom Hamiltonian H a1 , p and r are the momentum and position operators of an a...

Quantum fluctuations in the image of a Bose gas

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Cavity-induced chiral states of fermionic quantum gases

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