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Network of phase frustrated photon Bose-Einstein condensates

Marius Puplauskis, Violetta Sharoglazova, Carl Ulrich Mattschas, Chris Toebes, Jan Klaers

Published May 16, 2024• 0 citations
OpenAlex

Abstract

A novel approach to tackling computationally challenging problems involves utilizing a physical system of coupled Bose-Einstein condensates (BEC). The problem of finding a ground state of a network of BECs can be mapped in polynomial time to any problem of the NP-Complete class. In our network, we use photonic BECs (pBECs) [1] which rapidly reach their lowest energy state, typically within a fraction of a nanosecond, after which they can be subjected to interference to extract relative phases. These phases are then interpreted as a solution to the original problem. In our setup, we employ a cavity formed by two highly reflective Bragg mirrors, a dye serving as a thermalizing agent, and a green laser acting as a photon source. Additionally, by nanostructuring [2] one of the mirrors, we achieve transverse confinement of the pBECs. We will present our latest findings on a system of negatively coupled triangular arrangement of pBECs exhibiting spin frustration. References [1] J. Klaers, Nature 468, 545-548 (2010). [2] M. Vretenar, Advanced Optical Materials 11, 2202820 (2023).

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A novel approach to tackling computationally challenging problems involves utilizing a physical system of coupled Bose-Einstein condensates (BEC). The problem of finding a ground state of a network of BECs can be mapped in polynomial time to any problem of the NP-Complete class. In our network, we use photonic BECs (pBECs) [1] which rapidly reach their lowest energy state, typically within a fraction of a nanosecond, after which they can be subjected to interference to extract relative phases. These phases are then interpreted as a solution to the original problem. In our setup, we employ a cavity formed by two highly reflective Bragg mirrors, a dye serving as a thermalizing agent, and a green laser acting as a photon source. Additionally, by nanostructuring [2] one of the mirrors, we achieve transverse confinement of the pBECs. We will present our latest findings on a system of negatively coupled triangular arrangement of pBECs exhibiting spin frustration. References [1] J. Klaers, Nature 468, 545-548 (2010). [2] M. Vretenar, Advanced Optical Materials 11, 2202820 (2023).
Photon Bose-Einstein condensates (pBECs) are a platform of interest for both the study of fundamental phenomena in many-body physics and the implementation of next-generation analog simulators for solving optimization problems. In our physical system, the network of coupled pBECs in a microcavity setup is created by individually laser-pumping trap sites that are formed by permanent nanostructuring and connected via waveguides to their nearest neighbours. Due to the roughness and non-flat landscape of the microcavity mirrors, trap sites are excited at different frequencies, making the relative phases undefined. This is crucial for finding the ground state of a network of pBECs - a problem that is NP-complete, which makes this platform a promising candidate for analog optimization problem solver. We propose an approach for in-situ coherence tuning using a permanent nanostructuring technique with active feedback on excited trap site frequencies and report our preliminary results on the creation of an uncoupled coherent network of pBECs using this approach.
Bose-Einstein condensation (BEC) is a state of matter where bosons macroscopically\noccupy the ground state of a system. In 2010 the group of Martin Weitz achieved a\ntwo-dimensional Bose-Einstein condensation of photons by using a dye-filled micro-\ncavity. In 2015 our research group also achieved a photon BEC using a similar\nsetup. Although one expects the photons to be non-interacting, the radius of the\ncondensate has been shown to grow as a function of photon density. This implies\nrepulse photon-photon interactions. This leads us to question what the strength of\nthe interactions is.\nTo investigate the interaction strength we take single shot images of the photon gas,\nwhile varying the photon density in the cavity. From each image we determine the\nnumber of condensate photons and the radius of the condensate. Subsequently we de-\ntermine the interaction strength to be g = (6.6 +/- 0.7)E-3 and g = (8 +/- 1)E-2\nusing a dye concentration of 1.5 mM and 6.0 mM respectively. This implies that the\ninteraction strength increases for increasing dye concentration. The source of the\ninteractions is not yet understood and should be investigated further.\nWe also determine the polarization state of the photon gas. In order to do so we\nbuild an experimental setup which can measure all four Stokes parameters simulta-\nneously. Since the phase transition into Bose-Einstein condensation is an example of\nspontaneous symmetry breaking, one would expect the condensate to have a differ-\nent polarization each time it is created. We show that this is not the case and that\nevery newly created BEC has the same polarization state, i.e. linearly polarized in\nthe horizontal direction. We show this symmetry breaking is not affected by the dye\nconcentration, photon density inside the cavity or the cavity mirrors. It is however\ncaused by the intra-cavity polarization of the pump beam. We show that we can\nrotate the direction of the polarization by rotating the intra-cavity polarization of\nthe pump beam.
Bose-Einstein condensation (BEC) is the transition to a macroscopic occupation of the ground state of a system of bosonic particles. In 1995 the first experimental realization of BEC was achieved by condensing a dilute atomic gas [1,2]. It was long thought only massive particles could undergo BEC. However, in 2010 it was shown that photon BEC was achieved in an optical dye-filled microcavity [3]. In 2015, we became the second group to successfully repeat these experiments.\n\nBEC is a phase transition and thus it occurs at thermal equilibrium. To achieve a thermal photon gas the cavity is filled with a fluorescent dye solution. The dye molecules thermalize the photons by means of repeated absorption-emission cycles. We optically pump the cavity. With the pump we determine the number of photons absorbed by the dye, consequently defining a nonvanishing chemical potential. This ensures a conserved photon number. The photons are trapped by the harmonic potential induced by the concave cavity mirrors. Due to the cutoff energy determined by the cavity length, the trapped photons have a dispersion similar to that of a massive particle in a quantum harmonic oscillator. The cavity length is tuned such that the free spectral range is larger than the bandwidth of the dye. Therefore, only one longitudinal mode fits inside the cavity, making the photon gas effectively two-dimensional. We end up with a thermalized two-dimensional photon gas that has the eigenenergies of a quantum harmonic oscillator. The Bose-Einstein distribution function predicts a critical photon number. Pumping the thermal photon gas beyond this critical number will lead to photon BEC.\n\nWe measure the spectral- and spatial distributions of our two-dimensional photon gas. In both distributions we observe photon BEC. Results show the characteristics of a phase transition: the appearance of a sharp peak on top of the thermal cloud that coincides with a converging chemical potential to zero. Both the spectral- and spatial distribution are in agreement with the theoretical distribution of photons with an effective mass in a quantum harmonic oscillator. Expansion of the condensate has been measured. This could indicate nonlinear optical effects such as thermal lensing or repulsive photon-photon interactions.
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.
Abstract When particles with integer spin accumulate at low temperature and high density, they undergo Bose–Einstein condensation (BEC). Atoms, magnons, solid-state excitons, surface plasmon polaritons and excitons coupled to light exhibit BEC, which results in high coherence due to massive occupation of the respective system’s ground state. Surprisingly, photons were shown to exhibit BEC recently in organic-dye-filled optical microcavities, which—owing to the photon’s low mass—occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalize and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalization in our system where we can clearly distinguish laser action from BEC. Semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. In practical terms, photon BECs offer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages: the lack of dark electronic states in inorganic semiconductors allows these BECs to be sustained continuously; and quantum wells offer stronger photon–photon scattering. We measure an unoptimized interaction parameter ( g~\tilde{{{{{g}}}}}g~​ g ̃ ≳ 10–3), which is large enough to access the rich physics of interactions within BECs, such as superfluid light.
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.