Realizing arbitrary trapping potentials for light via direct laser writing of mirror surface profiles

Kurtscheid, Christian; Dung, David; Redmann, Andreas; Busley, Erik; Klaers, Jan; Vewinger, Frank; Schmitt, Julian; Weitz, Martin

doi:10.1209/0295-5075/130/54001

Cited by 24 publications

(31 citation statements)

References 18 publications

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“…In this experiment we use two methods for controlling the potential energy term. The first is a nanostructuring technique based on direct-laser writing that generates a well defined height profile on the mirror [42]. The second is precise adjustment of the tilt angle between the two cavity mirrors by piezo-electric actuation.…”

Section: Resultsmentioning

confidence: 99%

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Dispersive and dissipative coupling of photon Bose-Einstein condensates

Toebes¹,

Vretenar²,

Klaers³

2021

Preprint

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The synchronization of coherent states of light has long been an important subject of basic research and technology. Recently, a new concept for analog computers has emerged where this synchronization process can be exploited to solve computationally hard problems -potentially faster and more energy-efficient than what can be achieved with conventional computer technology today. The unit cell of such systems consists of two coherent centers that are coupled to one another in a controlled manner. Here, we experimentally characterize and analyze the synchronization process of two photon Bose-Einstein condensates, which are coupled to one another, either dispersively or dissipatively. We show that both types of coupling are robust against a detuning of the condensate frequencies and show similar time constants in establishing mutual coherence. Significant differences between these couplings arise in the behaviour of the condensate populations under imbalanced optical pumping. The combination of these two types of coupling extends the class of physical models that can be investigated using analog simulations.

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Section: Resultsmentioning

confidence: 99%

“…The microcavity is formed from two high-finesse mirrors, one of which is nanostructured using a direct-laser-writing method, see Ref. [42]. The height profiles of the mirror surfaces are determined via Mirau interferometry.…”

Section: Discussionmentioning

confidence: 99%

Dispersive and dissipative coupling of photon Bose-Einstein condensates

Toebes¹,

Vretenar²,

Klaers³

2021

Preprint

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“…S2 and ref. [22] for a detailed description of the method. We note that recent other work has reported an alternative technique to create potentials for microcavity photon gases, including box potentials, using focused ion beam milling [34].…”

Section: Potential Creationmentioning

confidence: 99%

“…One of the cavity mirrors exhibits a reflectivity maximum at 550 nm and a bandwidth of 50 nm, where the reflectivity is above 99.99%; in addition, it is equipped with an absorptive silicon layer below the highreflectivity Bragg coating, which enables nanostructuring of the mirror surface (see section "Potential creation" and ref. [22]). The opposing mirror consists of a custom dielectric coating, which contains two stacked reflection bands of 50 nm spectral width, the first one centered at 570 nm (on top; in contact with the dye), the second one around 700 nm (below; sandwiched between top-layers and glass substrate).…”

Section: Supplementary Information Experimental Schemementioning

confidence: 99%

“…To spatially confine the unbound plane-wave states of a 2D homogeneous system, we implement a box potential of size L as a container for the photons. The box potential is realized using a nanostructuring technique [21,22], which imprints a position-dependent static surface elevation onto one of the cavity mirrors. The locally reduced cavity length results in a repulsive potential.…”

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Compressibility and the Equation of State of an Optical Quantum Gas in a Box

Busley,

Miranda,

Redmann

et al. 2021

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The compressibility of a medium, quantifying its response to mechanical perturbations, is a fundamental property determined by the equation of state. For gases of material particles, studies of the mechanical response are well established, in fields from classical thermodynamics to cold atomic quantum gases. Here we demonstrate a measurement of the compressibility of a two-dimensional quantum gas of light in a box potential and obtain the equation of state for the optical medium. The experiment is carried out in a nanostructured dye-filled optical microcavity. We observe signatures of Bose-Einstein condensation at high phase-space densities in the finite-size system. Strikingly, upon entering the quantum degenerate regime, the measured density response to an external force sharply increases, hinting at the peculiar prediction of an infinite compressibility of the deeply degenerate Bose gas.Quantum gases of atoms, exciton-polaritons, and photons provide a test bed for many-body physics under both in-and out-of-equilibrium settings [1][2][3]. Experimental control over dimensionality, potential energy landscapes, or the coupling to reservoirs offer wide possibilities to explore different phases of matter. For cold atomic gases, thermodynamic susceptibilities and transport properties have been extracted from density measurements [4][5][6][7][8][9] and have proven to be direct manifestations of the equation of state (EOS). In general, the EOS of a material, e.g., its pressure-volume relation, describes both the thermodynamic state of a system under a given set of physical conditions as well as its response to perturbations, as mechanical compression.Experimental investigations of the EOS in quantum gases constitute a tool for the characterisation of phases and the identification of phase transitions, enabling important tests of physical models in a wide range of systems, from the ideal gas to superfluids and the interior of stars.Quantum gases of light have so far been experimentally realized in low-dimensional settings, mostly twodimensional (2D) systems [3]. Thermalized photon gases with non-vanishing chemical potential µ, as well as Bose-Einstein condensation (BEC) have been demonstrated in dye-filled optical microcavities at harmonic confinement [10][11][12], including measurements of density-insensitive thermodynamic quantities [13]. In contrast, the isothermal compressibility κ T = n −2 (∂n/∂µ) T at temperature T depends on the (local) particle density n in the gas; for a systematic study, it thus is desirable to avoid spatially inhomogeneous density distributions inherent to harmonically trapped gases, and instead prepare uniform samples, where applying a spatially uniform force directly allows one to compress the gas and probe κ T .

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Mirror Surface Nanostructuring via Laser Direct Writing—Characterization and Physical Origins

Vretenar

Puplauskis

Klaers

2023

Advanced Optical Materials

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advances to this method, perform timeresolved measurements of the process, and analyze its physical origins.Thanks to this novel nanostructuring method, open-access optical microcavities have become a very flexible platform for experiments with two-dimensional photon gases, in particular, for the study of lasing phenomena and photon Bose-Einstein condensation (BEC). [8][9][10][11][12][13] A major future application of such systems may be spin glass simulation, allowing the system to be used as a computing platform. [14] Furthermore, the study of polaritonic quantum gases based on open cavities [15,16] may benefit from this method. Beyond studying optical condensation phenomena, nanostructuring of high-reflectivity mirrors via laser direct writing may also find novel applications in areas such as cavity ringdown spectroscopy, [17] wavefront shaping, [18] and precision interferometry [19,20] (and references therein).In addition to the permanent modification of mirror surfaces, it is also desirable to perform time-dependent control over the transverse flow of light in microcavities. Mirrors with integrated piezo arrays, [21] heater arrays, [22] and electrostatic membranes [23] may be used for this purpose. As in the previously discussed case of permanent nanostructuring, [7] absorptive layers in the mirror also offer a solution to the problem of time-dependent control. This includes refractive-index tuning via laser writing of the thermo-responsive polymer poly(N-isopropylacrylamide) (pNIPAM) [24] added to the cavity medium, and thermal expansion of the mirror surface, which will be demonstrated in this paper. The former introduces an attractive potential, while the latter creates a repulsive potential. Since both techniques work on different timescales, they may be used in a complementary manner. Additionally, a certain degree of spatial complexity can be introduced by wavefront shaping the heating laser.The dielectric mirrors used in this work are produced using ion beam sputtering (IBS), and have the following composition: a fused silica substrate, atop which lies an optically absorptive amorphous silicon layer of 30 nm thickness, followed by a quarter-wave dielectric stack with a reflectivity maximum at a wavelength of 600 nm. In most measurements presented in this work, this dielectric stack consists of 20 pairs of Ta 2 O 5 and SiO 2 . However, we also evaluate thinner dielectric stacks with 11 and 10 pairs. The essential point of this mirror design is the absorptive Si layer that provides a way to locally heat the dielectric stack and the optical medium using laser light-which is the basis of all the phenomena we show in this paper. In the first part of this work, we will demonstrate that such mirrorsThe addition of an optically absorptive layer to otherwise standard dielectric mirrors enables a set of laser direct writing nanostructuring methods that can add functionality to such mirrors while retaining their high reflectivity. A thorough characterization of this method is given in this paper, and its physic...

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Realizing arbitrary trapping potentials for light via direct laser writing of mirror surface profiles

Cited by 24 publications

References 18 publications

Dispersive and dissipative coupling of photon Bose-Einstein condensates

Dispersive and dissipative coupling of photon Bose-Einstein condensates

Compressibility and the Equation of State of an Optical Quantum Gas in a Box

Mirror Surface Nanostructuring via Laser Direct Writing—Characterization and Physical Origins

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