The transition from a thermal cloud to a Bose–Einstein condensate (BEC) in an interacting ultra-cold Bose gas is a prototype in a universality class of diverse phase transitions. For a trapped ultra-cold Bose gas, we were able to study the critical regime both above and below the critical temperature with a Talbot–Lau interferometer, observing a peak in the correlation length. From this peak, we managed to determine the universal critical exponents for this phase transition as well as the finite-size and interaction corrections to the critical temperature. The results are all in quantitative agreement with theory. This work demonstrates the potential application of the Talbot–Lau interferometer to a wide range of critical phase transitions in ultra-cold atomic gases.
The transition from a thermal cloud to a Bose–Einstein condensate (BEC) in an interacting ultra-cold Bose gas is a prototype in a universality class of diverse phase transitions. For a trapped ultra-cold Bose gas, we were able to study the critical regime both above and below the critical temperature with a Talbot–Lau interferometer, observing a peak in the correlation length. From this peak, we managed to determine the universal critical exponents for this phase transition as well as the finite-size and interaction corrections to the critical temperature. The results are all in quantitative agreement with theory. This work demonstrates the potential application of the Talbot–Lau interferometer to a wide range of critical phase transitions in ultra-cold atomic gases.
We report the results of a study of measuring the correlation length at the Lambda critical phase transition point in an ultra-cold Bose gas with a temporal Talbot-Lau (TL) interferometery. Near the critical temperature, the correlation length increase exponentially and its critical exponent factor is measured around 0.67, which is a universal value in quantum gas. In the experiment we filtered the fraction of condensate from the thermal cloud at the Lambda critical phase transition point by means of the TL interferometer technique.
Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle interactions fall into the XY model universality class, the ideal Bose gas has been predicted to form a distinct universality class whose signatures have not yet been revealed experimentally. Here, we report the observation of critical scaling in a two-dimensional trapped quantum gas of essentially noninteracting photons, which thermalize by radiative contact to a reservoir of molecules inside a microcavity. By measuring the spatial correlations near the condensation transition, we determine the critical exponent for the correlation length to be ν=0.52(4). Our results constitute a first experimental test of the long-standing scaling predictions for the Bose gas universality class.
The phase transition of Bose-Einstein condensation was studied in the critical regime, where fluctuations extend far beyond the length scale of thermal de Broglie waves. We used matter-wave interference to measure the correlation length of these critical fluctuations as a function of temperature. Observations of the diverging behavior of the correlation length above the critical temperature enabled us to determine the critical exponent of the correlation length for a trapped, weakly interacting Bose gas to be nu = 0.67 +/- 0.13. This measurement has direct implications for the understanding of second-order phase transitions.
The study of second-order phase transitions is a broad research theme that provides fundamental insights into the physical nature of complex systems. A central aspect deals with the concept of universal behavior. Universality governs, for example, the diverging correlated fluctuations of an order parameter, characterized by a macroscopic correlation length ξ, as well as the divergence of other thermodynamic quantities near the critical point. Extracting the critical exponents associated with these diverging quantities shows that quite different physical systems can exhibit identical scaling behavior, placing them into common universality classes. Bose-Einstein condensation of an ideal (i.e., non-interacting) gas of bosons is a second-order phase transition, and thus provides a valuable platform to investigate universal critical behavior in the quantum gas regime, driven purely by quantum statistics rather than inter-particle interactions. While historically studied in ultracold atomic and molecular gases, Bose-Einstein condensation can now be realized in a two-dimensional photonic gas at room temperature using dye-filled microcavities. The microcavity imposes a low-energy cutoff, providing a non-vanishing ground state and an effective mass for the intracavity photons, which thermalize via repeated absorption and emission processes with the dye reservoir rather than inter-particle interactions. Consequently, this platform establishes an almost perfectly ideal, two-dimensional quantum gas of light. In combination with versatile trapping techniques, it provides a highly tunable platform to explore the thermodynamics of quantum gases. This thesis presents a quantitative study of spatial correlations in a uniformly trapped two-dimensional photon gas. The uniform confinement is achieved by a custom mirror-structuring technique, resulting in box-like trapping potentials. The temporal and spatial coherence properties of the gas are validated in both the thermal and condensed regimes using an interferometric measurement technique. Because the applicability of scanning interferometry limits measurements of critical scaling behavior, an alternative method is introduced to extract the first-order spatial coherence directly from the far-field angular distribution of the cavity emission in a single experimental shot. This technique enables the extraction of the spatial correlation length ξ and a precise evaluation of its scaling behavior in the vicinity of the critical point Nc. The measurements presented here demonstrate, for the first time, the determination of a critical exponent in the (ideal) Bose gas universality class. The obtained critical exponent of ν = 0.52 ± 0.04 for the two-dimensional ideal Bose gas is consistent with theoretical expectations. Crucially, this critical exponent is found to be robust and independent of the system size within experimental uncertainties, demonstrating the universality of the scaling behavior. Finally, the limits of this universal behavior are explored by demonstrating the breakdown of critical scaling when the thermalizing coupling between the photons and dye molecules in the cavity is reduced, driving the photon gas out of thermal equilibrium.
Summary form only given. Phase transitions are among the most dramatic phenomena in nature. Minute variations in the conditions controlling a system trigger a fundamental change of its properties. In the critical regime near a second-order phase transition point the fluctuations of the order parameter are so dominant that they completely govern the behaviour of the system on all length scales. The correlation length of the ultracold gas measures the characteristic length scale of these fluctuations and diverges at the critical temperature. Using cold atomic gases, we have directly observed critical fluctuations of the order parameter near the phase transition of Bose-Einstein condensation. From the divergence of the correlation length of the order parameter versus temperature we have determined its critical exponent v. Despite our densities being ten orders of magnitude smaller and our interactions considerably weaker, we find a remarkable similarity to case of the lambda-transition of helium-4.
Quantum criticality emerges when the collective fluctuations of matter undergo a continuous phase transition at zero temperature and has been a research focus in conventional condensed-matter physics over the past several decades. In the quantum critical regime, the exotic and universal properties are expected. These properties are independent of the microscopic details of the system, but depend only on a few general properties of the system, such as its dimensionality and the symmetry of the order parameter. The research of quantum criticality can not only help us to understand quantum phase transitions, but also provide a novel route to new material design and discovery.Ultracold bosonic gases have provided a clean system for studying the quantum critical phenomena. The critical behavior of a weakly interacting three-dimensional (3D) Bose gas should be identical to that of 4He at the superfluid transition, which belongs to the 3D XY universality class. From the normal fluid to the superfluid, the system undergoes a phase transition from completely disorder to long-range order, while in the vicinity of the phase transition point, the system parameters will show some singularity characteristics. In this paper, we observe the critical behavior of 87Rb Bose gas in a quadrupole-Ioffe configuration (QUIC) trap near the phase transition temperature Tc. A novel singularity behavior of the full width at half maximum of momentum distribution (FWHMMD) of atomic gas is discovered in the experiment. Prior to our experiment, we prepare a sample with 7.8105 87Rb atoms in the 5S1/2 |F=2, mF=2 state. Then the sample is held in a QUIC trap for a presetting period of time to control the temperature of atom sample precisely. During the holding time, the sample is heated up due to background gas collisions or fluctuations of the trap potential. In our experiment, the heating rate is deduced to be 0.3480.078 nK/ms from the absorption image. For a bosonic gas in a harmonic trap, critical gas can only cover a finite-size region due to a spatially varying density. We define the finite-size region as a critical region determined by the Ginzburg criterion. Then the FWHMMDs of atomic gas in the critical region are measured for different temperatures near the critical point. To this aim, we first extract the momentum distribution of atomic gas from the absorption image of the atomic clouds released from the QIUC trap after free expansion. Thus momentum distribution of atomic gas in the critical region can be extracted from the absorption image by subtracting the momentum distribution of thermal gas outside the critical region. According to the statistical results of the FWHMMD at different temperatures, we find that the FWHMMD suddenly reduces, thus revealing a very notable singularity behavior when the temperature is very close to the phase transition temperature Tc.