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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Bose-Einstein Condensation of Photons in a Four-Site Lattice Potential

Andreas Redmann, Niels Wolf, Frank Vewinger, Julian Schmitt, Martin Weitz

Published Jun 26, 2023• 0 citations
Publisher

Abstract

Bose-Einstein condensation can be observed with e.g. ultracold atomic gases, polaritons, and since about a decade ago also with low-dimensional photon gases [1]. Cold atomic gases in lattice potentials are usually prepared following the creation of a condensate by transferring it into the periodic potential, while in recent work with photon gases direct condensation into a coherently split state of light has been realized [2]. Here we report on experimental work directed at realizing thermalized photon gases in periodic potentials of increased complexibility, i.e. beyond a double well.

DOI
10.1109/cleo/europe-eqec57999.2023.10232453

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Bose-Einstein condensation can be observed with e.g. ultracold atomic gases, polaritons, and since about a decade ago also with low-dimensional photon gases [1]. Cold atomic gases in lattice potentials are usually prepared following the creation of a condensate by transferring it into the periodic potential, while in recent work with photon gases direct condensation into a coherently split state of light has been realized [2]. Here we report on experimental work directed at realizing thermalized photon gases in periodic potentials of increased complexibility, i.e. beyond a double well.
Bose-Einstein condensation has in the last two decades been observed in cold atomic gases and in solid-state physics quasiparticles, exciton-polaritons and magnons, respectively. The perhaps most widely known example of a bosonic gas, photons in blackbody radiation, however exhibits no Bose-Einstein condensation, because the particle number is not conserved and at low temperatures the photons disappear in the system’s walls instead of massively occupying the cavity ground mode. This is not the case in a small optical cavity, with a low-frequency cutoff imprinting a spectrum of photon energies restricted to values well above the thermal energy. The here reported experiments are based on a microscopic optical cavity filled with dye solution at room temperature. Recent experiments of our group observing Bose-Einstein condensation of photons in such a setup are described. Moreover, we discuss some possible applications of photon condensates to realize quantum manybody states in periodic photonic lattices and photonic Josephson devices.
Thermalization of radiation by contact to matter is a well-known concept, but the application of thermodynamic methods to complex quantum states of light remains a challenge. Here, we observe Bose-Einstein condensation of photons into the hybridized ground state of a coupled four-site ring potential. In our experiment, the periodically closed ring lattice superimposed by a weak harmonic trap for photons is realized inside a spatially structured dye-filled microcavity. Photons thermalize to room temperature, and above a critical photon number macroscopically occupy the symmetric linear combination of the site eigenstates with zero phase winding, which constitutes the ground state of the system. The mutual phase coherence of photons at different lattice sites is verified by optical interferometry.
Bose-Einstein condensation, the macroscopic ground state occupation of bosonic particles at low temperature and high density, has previously been observed for cold atomic gases and solid-state quasiparticles. In recent work, Bose-Einstein condensation of photons has been realized in a dye-filled optical microcavity at room temperature [1, 2]. The short mirror spacing of the curved mirror microcavity introduces a low-frequency cutoff, and thermal contact to the dye-solution is achieved by subsequent absorption and re-emission processes.
The advent of controlled experimental accessibility of Bose-Einstein condensates, as realized with e.g. cold atomic gases, exciton-polaritons, and more recently photons in a dye-filled optical microcavity, has paved the way for new studies and tests of a plethora of fundamental concepts in quantum physics. We here describe recent experiments studying a transition between laser-like dynamics and Bose-Einstein condensation of photons in the dye microcavity system. Further, measurements of the second-order coherence of the photon condensate are presented. In the condensed state we observe photon number fluctuations of order of the total particle number, as understood from effective particle exchange with the photo-excitable dye molecules. The observed intensity fluctuation properties give evidence for Bose-Einstein condensation occurring in the grand-canonical statistical ensemble regime.
In this thesis I report on experiments that enter a new regime in the many body physics of ultracold atomic gases. A Bose-Einstein condensate is loaded into a three-dimensional optical lattice potential formed by a standing wave laser light field. In this novel quantum system we have been able to both realize a quantum phase transition from a superfluid to a Mott insulator, and to observe the collapse and revival of a macroscopic matter wave field. Quantum phase transitions are driven by quantum fluctuations and occur, even at zero temperature, as the relative strength of two competing energy terms in the underlying Hamiltonian is varied across a critical value. In the first part of this work I report on the observation of such a quantum phase transition in a Bose-Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. In the superfluid ground state, each atom is spread-out over the entire lattice, whereas in the Mott insulating state, exact numbers of atoms are localized at individual lattice sites. We observed the reversible transition between those states and detected the gap in the excitation spectrum of the Mott insulator. A Bose-Einstein condensate is usually described by a macroscopic matter wave field. However, a quantized field underlies such a "classical" matter wave field of a Bose-Einstein condensate. The striking behavior of ultracold matter due to the field quantization and the nonlinear interactions between the atoms is the focus of the second part of this work. The matter wave field of a Bose-Einstein condensate is observed to undergo a series of collapses and revivals as time evolves. Furthermore, we show that the collisions between individual pairs of atoms lead to a fully coherent collisional phase shift in the corresponding many-particle state, which is a crucial cornerstone of proposed novel quantum computation schemes with neutral atoms. With these experiments we enter a new field of physics with ultracold quantum gases. In this strongly correlated regime, interactions between atoms dominate the behavior of the many-body system such that it can no longer be described by the usual theories for weakly interacting Bose gases. This novel quantum system offers the unique possibility to experimentally address fundamental questions of modern solid state physics, atomic physics, quantum optics, and quantum information.
Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.