Quarterly Report II/2021

OSCAR Reports
an SFB/TR 185 magazine

Second Funding Period, Issue 4
Author: Prof. Dr. Georg von Freymann


Observation of a non-Hermitian phase transition in an optical quantum gas

Fahri Emre Öztürk, Tim Lappe, Göran Hellmann, Julian Schmitt, Jan Klaers, Frank Vewinger, Johann Kroha, Martin Weitz
Science 372, 88 (2021)

Photon Bose-Einstein-Condensates (BEC) and common lasers share at first sight the same collection of components: a cavity, a gain medium and a pump source. While photon BEC operate near thermal equilibrium, lasers operate far away from thermal equilibrium. Hence, one might expect a smooth transition from one to the other regime of operation, as both phenomena exhibit spontaneous symmetry breaking. In a photon BEC photons are trapped in a dye-filled microcavity (A). The cavity losses are compensated by external pumping of the dye molecules. Via photon emission from the dye into the cavity and subsequent reabsorption by the dye, the photon gas thermalizes, leading to a spectral distribution which closely follows the Bose-Einstein distribution at room temperature (B). Our OSCAR colleagues in Projects A5 and C4 could now reveal a phase transition in the photon BEC occurring way before the transition to the lasing phase happens.

The dissipative coupling to the environment in open quantum systems as the photon BEC is described by a non-Hermitian time-evolution operator, which exhibits complex eigenvalues. Such operators show exceptional points, at which the eigenvalues and the corresponding eigenmodes coalesce. Exceptional points are an indication of phase transitions. To experimentally identify exceptional points in the system, the photon number correlation g(2) is measured by removing the polarization degeneracy of the cavity emission via a polarizer and filtering it for real space as well as momentum by two pin-holes in front of a fast photomultiplier.
Varying the pump power allows for populating condensates with increasing mean photon number. The mean photon number controls the effective losses as well as the oscillation frequency of the undamped cavity and thus allows for a detailed mapping of the different phases. At a mean photon number of approximately 2,800 the exceptional point is found (C), separating a BEC phase with biexponential decay from a BEC phase with oscillatory behavior.

Thus, OSCAR researchers could reveal a state of the light field in photon BEC, that is separated by a dissipative phase transition from a biexponential to an oscillatory phase and that is distinctly different from the phenomenon of lasing.


Stimulated-Raman-adiabatic-passage mechanism in a magnonic environment

Qi Wang, Thomas Brächer, Michel Fleischhauer, Burkard Hillebrands, and Philipp Pirro
Applied Physics Letters 118, 182404 (2021)

Model systems play an important role in experimentally realizing quantum phenomena and allowing thus the direct observation of otherwise microscopic phenomena, which are difficult to be experimentally addressed. One exemplary model system especially suited for implementing tight-binding physics consists of an array of coupled waveguides. The propagation direction along the waveguides plays the role of the time-evolution, which can directly be seen in the mathematical analogy between the paraxial Helmholtz equation and the time-dependent Schrödinger equation. Designing the shape and the distance between waveguides not only allows for tuning the hopping terms between the lattice sites but also for establishing artificial gauge fields which very precisely control the flow of light in the system.

In this publication researcher from the collaborative research center SPIN+X team up with OSCAR PI Michael Fleischhauer to realize the stimulated-Raman-adiabatic-passage mechanism (STIRAP) known from atomic physics in a model system based on coupled waveguides. Instead looking at the usual plasmonic or dielectric waveguides employed in OSCAR, the waveguides shown in (a) guide magnons, i.e., fundamental excitations of the spin system. The material used is Yttrium Iron Garnett (YIG), one of the most promising materials for magnonic computation due to its very low damping constant.


The STIRAP process transfers excitation from a ground state to an excited state via an intermediate state, which is not populated during this transfer. Counterintuitively, one first couples the unpopulated excited state with the unpopulated intermediate state via a laser pulse, before another pulse couples the populated ground state with the intermediate state.
This counterintuitive scheme has now been directly realized in the waveguide configuration shown in (a). The three waveguides from top to bottom correspond to the excited state (W1), the intermediate state (W2), and the ground state (W3). Excited state and intermediate state are first coupled by reducing the distance between these waveguides before the coupling between ground state and intermediate state is switched on. This allows for transferring the propagating spin wave from the ground state waveguide W3 to the excited state waveguide W1 without populating the intermediate waveguide W2 at all. As in atomic physics it forms a dark state and again demonstrate the universal power of model systems.

Observation of first and second sound in a BKT superfluid

Panagiotis Christodoulou, Maciej Galka, Nishant Dogra, Raphael Lopes, Julian Schmitt, and Zoran Hadzibacic
Natue 594, 191 (2021)

Observing first and second sound in a fluid is a strong indication of its superfluidity. The origin of the two sounds can be found in the hydrodynamic two-fluid theory, which describes fluids below their critical temperature. Here, fluids are described as a mixture in thermodynamic equilibrium of a superfluid component and a viscous normal component, which carries the entropy. In suprafluid Helium the higher-speed first sound is found to be a pure density wave while the lower-speed scond sound is a pure entropy wave. Observing the second sound is a clear indication of superfluidity. So far, the observation of second sound in two-dimensional superfluid Helium has been hindered by the viscous normal component being pinned to the substrate.

Using a homogeneous two-dimensional 39K Bose gas, the observation of first and second sound has been finally achieved by a group of researcher including OSCAR PI Julian Schmitt. The two-dimensional gas is prepared by elaborate trapping potentials as shown in (b). The excited density wave can be observed in the time-resolved absorption image of the two-dimensional gas. The system is driven by a spatial uniform force created by a magnetic field gradient. In resonance driving force and resulting oscillation are π/2 out of phase, as shown in (c). Analyzing the data for different driving frequencies at different temperatures below and above the critical temperature clearly reveals the two sounds for temperatures below the critical temperature while this signature vanishes above the critical temperature, showing only first sound.

With this experiment the first ever demonstration of second sound in a two-dimensional atomic gas was succesful. Even for such unconventional BKT supderfluids the two-fluid model is applicable. Proceeding to even lower temperatures might show the expected hybridazition of first und second sound.