Author: Ameneh Sheikhan
Ultracold Bose Gases in Dynamic Disorder with Tunable Correlation Time (B5)
Benjamin Nagler , Martin Will , Silvia Hiebel, Sian Barbosa, Jennifer Koch, Michael Fleischhauer, and Artur Widera
Phys. Rev. Lett. 128, 233601 (2022)
A lot is known about static disorder which leads to Anderson localization in theory and experiment. Theoretically the dynamical noise has been studied in classical models where the noise in space and time leads to a non-equilibrium phase transition to a symmetry breaking state which is controlled by both the correlation time and the correlation length of the noise. In quantum regime the steady state might be more complicated. In the paper by Nagler et al. they investigate the non-equilibrium dynamics of ultra cold Bose gas which is subjected to the dynamical disorder. In their experiment they have a cigar shaped cloud of bosonic gas of Lithium molecules where with Feshbach resonance they tune the s-wave scattering length and the binding energy. The statice disorder can be realized with a repulsive optical speckle potential which is created by sending a laser through a diffusive plate with random surface structures. To generate the dynamical disorder the laser beam is sent through two plates with random structure where one plate is rotating against the other one. Then the laser beam is focused to the atomic cloud. As the position of scatterers change in time by rotating one of the plates the induced optical potential is random in time and position with known correlation length in position and time. The intensity of the disorder is the average speckle potential in the cloud.
First the authors investigate the thermal cloud in the dynamical disorder. The speckled potential is on for different hold times and the temperature is measured from the integrated density distribution. The temperature increases which is linearly depending on the holding time and one can measure the heating rate. The experiment is repeated for different correlation time of the dynamical disorder. The heating rate is related to the inverses of correlation time which is in good agreement with the numerical simulation of classical thermal noninteracting particles.
Next the authors study the cold quantum gas in the dynamical disorder. The number of molecules are measured for different holding times as before where it is linearly decreasing. Thus the loss rate is calculated and repeated for different correlation times. The loss rates increases with the inverse of correlation time. They contribute two main processes to the loss of molecules from the cloud. (i)The dynamical disorder heats up the cloud which transfer some molecules from the BEC condensate to the thermal cloud where they can scape. (ii) In the other process the speckle potential excite molecules in the condensate which leads to the decrease of condensate fraction due to the Landau damping. Using models including these processes they compare the experimental data with theory. Their finding is that at large correlation times the losses due to the excitations in the condensate is negligible, but for smaller values of correlation time both loss processes are playing a role.
With this experimental setup the authors have established a platform to investigate the strongly interacting classical and quantum systems in dynamical disorder.
Observation of the Wannier–Stark ladder in plasmonic waveguide arrays (C4)
Helene Wetter, Zlata Fedorova, and Stefan Linden
Opt. Lett. 47, 3091-3094 (2022)
Subjecting an external electric field to electrons in a periodic potential leads the the so called Bloch oscillations where electrons oscillate in time. In the presence of external field the extended Bloch states turn into spatially localized Wannier-Stark states. Equivalently in the spectrum the continuous Bloch band turns into the equally spaced energy levels where the energy difference is related to the inverse of the Bloch oscillation period. This is known as the Wannier-Stark ladder.
Wetter et al. in the group of Stefan Linden investigate the propagation of surface plasmon polaritons in arrays of dielectric loaded surface plasmon polariton waveguides with an effective external potential. Engineering the geometry of the waveguides they are able to simulate the plasmonic analog of the Bloch oscillation of an electron in the lattice subjected to an external field and observe Wannier–Stark ladder. The waveguides are equally distanced along x-direction to simulate the homogenous hopping amplitude and the gradient of the height of the waveguides mimics the applied field. In their experimental setup they are able to have a linear growth of the height in the central part of the waveguides array. The surface plasmon polariton propagates spatially along x and z direction and its propagation is governed by an equation which describes the dynamical propagation of an electron in the tight binding model in one dimension where the direction z plays the role of time and thus the momentum in this direction is equivalent to energy for electrons. Measuring the transmitted laser beam and the surface plasmon polariton which are filtered out using Fourier filtering, they have access to the time-dependent density distribution and the momentum resolved spectrum.
As a start they consider waveguide array with no height gradient and they observe the almost cosine shape in the spectrum as expected in the tight binding model. In the next step they excite single waveguide in the center of the array and observe periodic breathing of the density distribution in time (z direction). In the spectrum one sees discrete modes which are extended along the momentums in x direction which indicates that these modes are spatially localized. The modes are equally distanced and as expected the energy difference between each mode is related to the breathing mode of the the Bloch oscillations they measure.
To excite more of the localized Wannier Stark states they excite multiple waveguides, creating wave packet of Gaussian shaped exciting about seven waveguides. In this case the time-periodic Bloch oscillations is in the form of sinusoidal oscillations of the density distribution instead of the coherent breathing mode as seen in case with single waveguide excitation. The Wannier-Stark ladder with seven rungs are observed in the spectrum and as before the energy difference is related to the oscillating period of plasmons in the time (z direction). To support their experimental findings the authors numerically simulated the discrete model and get similar results as in the experiment.
Nonlocality-induced surface localization in Bose-Einstein condensates of light (B1, B6)
Marcello Calvanese Strinati, Frank Vewinger, and Claudio Conti
Phys. Rev. A 105, 043318 (2022)
In the recent experiments the Bose-Einstein condensation (BEC) of photonic gas in the dye-filled micro-cavities has been realized. In these experiments an optical quantum gas is trapped between two cavity mirrors where by pumping more photons into the cavity the BEC emerges. By engineering the geometry of the cavity mirrors it is possible to achieve the desired mass and effective potential of arbitrary shape for example the harmonic confinement, the double-well potential or the box potential. In the photonic gas there are two types of photon-photon interactions, the thermo-optical induced interactions which are non-local and can have arbitrary range of interaction. There exists also the effective local attractive photon interaction caused by the optical Kerr effect which is small compared to the thermo-optical interaction and thus negligible. In the micro-cavity experiments so for mainly the short range interaction of photons is considered. In this article, the authors investigate analytically and numerically the effect of the photon-photon interaction with arbitrary range in different external potentials to see how the strong interaction of photons with longer range affect the condensate properties.
The local photon density which is measured by imaging the cavity emission is considered effectively as a steady state. This steady state can be described by the wave function which is position dependent and obeys the time-independent Gross-Pitaevskii (GP) equation where the chemical potential quantifies the energy stored in the condensate of photonic gas and also the mass, the external potential and the non-local interaction are known. The interaction adds a non-linear term into the GP equation.
The authors consider a non-local interaction in the one dimensional GP equation which is repulsive and has the form of a reqularized box potential with a parameter and which quantify the range and intensity of interaction respectively. They first consider a double-well potential where there is a double-well in the middle of a harmonic confinement which is very close to the data from the double-well potential in the experiment. Using the Newton-Raphson method they simulate the discretized GP equation. With local interaction or interactions with ranges smaller than the condensate size, the symmetric state has the lowest energy with a non-zero density at the center and the anti-symmetric state has higher energy and has a node at the center. For interaction ranges comparable to the condensate size, the non-local interaction suppresses the overlap of two condensate in each well and induces a depletion area in the center where the symmetric and antisymmetric states have similar spatial shape and the symmetric-antisymmetric level inversion occurs. Thus the ground state which was initially symmetric with non-zero density at the center, transforms into the anti-symmetric state with two condensates localized more at the surfaces by increasing the strength of the interaction. For interaction ranges much larger than the condensate size, the effect of the interaction is trivial and can be indicated as an energy shift in the GP equation.
In the next step the authors investigate the interplay between the strength and the range of interaction for one-dimensional system with more (six) wells where four non-degenerate bulk states and two quasi-degenerate surface states exist. For non-interacting case the surface states have higher energy compared to the bulk states. As before for local interaction () or interaction with a range smaller than the condensate size, there is no level inversion by changing the strength of the interaction. For the interaction range comparable to the condensate size (), the level inversion occurs and the surface localization is induced by the non-local interaction i.e. the surface states initially with the highest energy become the ground state for strong interactions. For larger range of interaction the level inversion and thus the surface localization does not occur. With this work the authors successfully show that the non-local interaction can lead to visible effects in the chains of BECs.
