Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics

Abstract

Studies of ultracold gases in optical lattices1 link many disciplines. They allow testing fundamental quantum many-body concepts of condensed-matter physics in well controllable atomic systems 1 , e.g., strongly correlated phases, quantum information processing. Standard methods to observe quantum properties of Bose-Einstein condensates (BEC) are based on matter-wave interference between atoms released from traps 2,3,4,5,6 , destroying the system. Here we propose a new, nondestructive in atom numbers, method based on optical measurements, proving that atomic quantum statistics can be mapped on transmission spectra of high-Q cavities, where atoms create a quantum refractive index. This can be extremely useful for studying phase transitions 7 , e.g. between Mott insulator and superfluid states, since various phases show qualitatively distinct light scattering. Joining the paradigms of cavity quantum electrodynamics (QED) and ultracold gases will enable conceptually new investigations of both light and matter at ultimate quantum levels. We predict effects accessible in experiments, which only recently became possible 8 . All-optical methods to characterize atomic quantum statistics were proposed for homogeneous BEC 9,10,11,12,13 and some modified spectral properties induced by BEC's were attributed to collective emission 9,10 , recoil shifts 12 or local field effects 14 . We show a completely different phenomenon directly reflecting atom quantum statistics due to statedependent dispersion. More precisely, the dispersion shift of a cavity mode depends on the atom number. If the atom number in some lattice region fluctuates from realization to realization, the modes get a fluctuating frequency shift. Thus, in the cavity transmission-spectrum, resonances appear at different frequencies directly reflecting the atom number distribution function. Such a measurement allows then to calculate atomic statistical quantities, e.g., mean value and variance reflected by spectral characteristics such as the central frequency and width.Different phases of a degenerate gas possess similar mean-field densities but different quantum amplitudes. This leads to a superposition of different transmission spectra, which e.g. for a superfluid state (SF) consist of numerous peaks reflecting the discreteness of the matter-field. Analogous discrete spectra reversing the role of atoms and light, thus reflecting the photon structure of electromagnetic fields, were obtained in cavity QED with Rydberg atoms 15 and solid-state superconducting circuits 16 . A quantum phase transition towards a Mott insulator state (MI) is characterized by a reduc- tion of the number of peaks towards a single resonance, because atom number fluctuations are significantly suppressed 17,18 . As our detection scheme is based on nonresonant dispersive interaction independent of a particular level structure, it can be also applied to molecules 19,20 .We consider the quantized motion of N two-level atoms in a deep periodic optical lattice with M sites formed by far off-reso...

Self-ordering dynamics of ultracold atoms in multicolored cavity fields

“…8. Extra peaks appearing for higher pump strengths in the resonance curve indicate different pair correlations of the atoms as discussed in some detail in [29] and can be seen in the spatial density correlations visualized in fig. 9.…”

Strong atom–field coupling for Bose–Einstein condensates in an optical cavity on a chip

“…This is an important improvement for applications such as the quantum memory. Furthermore, BEC-cQED experiments such as ours and a simultaneous similar one 12 can be used to study BECs in the regime of very small atom numbers where the mean-field approximation breaks down, and may allow observation of effects such as a predicted slight modification of the refractive index of the atomic sample close to the BEC transition 20 , and differences between quantum phases in transmission spectra of cavities containing a degenerate gas in an optical lattice 21 .…”

Mean-field dynamics of a Bose Josephson junction in an optical cavity

“…In the limit of large detuning [16] and weak pump, the atom field interaction is of dispersive nature, and the two-level atoms can be treated as scalar particles with the upper level being adiabatically eliminated. Under the two-mode approximation for the atoms, the interaction between the atoms and the cavity mode is [17],…”