Квантовые вихри и их массивы в поляритонных конденсатах, сформированных внутри оптических ловушек/Quantum vortices and their arrays in optically trapped polariton condensates тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Ситник Кирилл Александрович

• Ситник Кирилл Александрович
• кандидат наук
• 2024

Оглавление диссертации кандидат наук Ситник Кирилл Александрович

Table of content

Page

Introduction

Chapter 1. Physics of planar microcavities

1.1 Distributed Bragg Reflectors

1.2 Confined light in planar microcavities

1.3 Excitons in quantum wells

1.4 Light-matter strong coupling in planar microcavities

1.5 Bose-Einstein condensation of polaritons

1.5.1 Bose statistics for elementary particles

1.5.2 Critical temperature for Bose condensates. Statistical

approach

1.5.3 Critical temperature for Bose condensates. Quantum mechanical approach

1.5.4 Signatures of microcavity polaritons condensation

1.5.5 Mechanism of microcavity polaritons condensation

1.6 Optically trapped polariton condensates

1.7 Polariton superfluidity

1.8 Vortices in polariton condensates

1.9 Chapter summary

Chapter 2. Experimental methods and techniques

2.1 Interferometry

2.1.1 Introduction to interferometry

2.1.2 Homodyne interferometry with plane reference wave

2.2 Holography

2.2.1 Introduction to holography

2.2.2 Off-axis digital holography for phase and intensity reconstruction

2.2.3 Digital holography with spatial light modulators

2.2.4 Gaussian beam shaping to the ring profile

2.3 Microcavity sample

2.4 Imaging techniques

2.5 Experimental setup

2.6 Chapter summary

Chapter 3. Charge-oscillating vortex cluster

3.1 Vortex clusters

3.2 Observation of trapped polariton condensate with non-trivial

intensity distribution

3.3 Spatial modes detection with homodyne interferometry

3.4 Ince-Gaussian modes

3.5 First order correlations measurements

3.6 Polarization-resolved real-space imaging

3.7 Temporal dynamics of vortex cluster

3.8 Numerical simulation of polariton condensate in the elliptic potential

3.9 Control of topological charge oscillation frequency

3.10 Chapter summary

Chapter 4. Vortex clusters in rotating potentials

4.1 Experimental realization of bichromatic rotating beam

4.2 Formation of the single-charged vortex in the rotation trap

4.3 Formation of the vortex clusters in rotating traps

4.4 Numerical simulation of polariton condensate in rotating potentials

4.5 Vortex number control by excitation power

4.6 Chapter summary

Conclusion

Acknowledgements

Glossary

References

Other author's publication not included in this thesis

List of figures

Введение диссертации (часть автореферата) на тему «Квантовые вихри и их массивы в поляритонных конденсатах, сформированных внутри оптических ловушек/Quantum vortices and their arrays in optically trapped polariton condensates»

Introduction

In order to solve more and more challenging calculation problems, humanity has been actively developing electronics during the last century. At the same time, the communication lines demanded a higher speed (bandwidth) of information transfer caused by the enormous growth of the number of electronic devices and the necessity to provide stable and fast enough communication between them.

One of the possible ways to increase the communication bandwidth is the utilization of light instead of electrons. The possibility of using optics for communication systems was first demonstrated in 1966 [1]. However, the production of optical fibers at that time was a technologically difficult task. Besides this, compact and powerful coherent light sources were only discovered in 1962 [2]. As a result, the commercial implementation of optical communication lines began only in the 1980s.

Nowadays, a huge amount of information is transmitted via optical communication lines, with bandwidth approaching its limit. Modern solutions to this problem concentrate on the utilization of additional light degrees of freedom. The latter includes the wavelength [3], polarization [4] and the orbital angular momentum (OAM) [5] of light. These features of the transmitted signal allow for multiplexing more channels into one inside the fiber without interference between them. Unlike polarization and wavelength modulation, which are now widely used, the utilization of the OAM degree is still at the level of a promising concept.

A prominent example of a light state, carrying the OAM, is the so-called vortex beam. This state is characterized by a hollow core intensity distribution and quantized OAM. Current interest in vortex beams is caused by their practical applications, such as optical cryptography [6], optical tweezers [7], particle manipulation in 3D [8, 9], DNA structure modification [10], optical microscopy overcoming the Rayleigh resolution limit [11].

The optical beams comprising vortex structures, their combinations, and sophisticated phases are usually called structured light. There are several approaches for the generation of such light states, for example, higher-order modes interference may result in vortex crystal formation [12, 13, 14, 15]. Another widely used approach is the utilisation of conventional phase modulators (spatial light modulators,

phase plates) [16]. All of these methods require lasers as the source of coherent emission. However, optical vortex structures, once created, do not interact with each other due to the non-interacting nature of photons. The coupling between objects with phase dislocations has potential in, for example, analog optical simulation and computing. One of the prospects for the realization of this is the hybridization of light and matter. Such a platform allows one to introduce the interaction between particles, forming the coherent states while preserving optical control.

An example of a macroscopic coherent state with weak interaction between particles is the Bose-Einstein condensate (BEC) of cold atoms [17]. However, even after almost 30 years since the first experimental BEC realization, the precise control of the states is still an extremely challenging task. Hybrid light-matter quasiparticles (exciton-polaritons) [18] are an alternative testbed offering opportunities to control the interaction on the one hand and relative simplicity of state characterization on the other hand.

Polaritons are composite bosons appearing in the strong coupling regime between microcavity photons and matter excitons. They have several unique features such as (1) possibility to interact with each other [19, 20] (2) low effective mass; (3) possibility to form the the macroscopic coherent states, called polariton condensates [18]; (4) condensation could be achieved at several degrees of Kelvins for inorganic materials, and even at room temperatures for organic microcavities [21]; (5) polaritons could be optically controlled by optical methods [22, 23, 24, 25, 26].

Polariton condensates are nice platform for the experimental investigation of superfluidity [27], quantized vortices [28], half-quantized vortices [29]. Furthermore, they could be utilized for engineering the giant vortex states [30], to implement neuromorphic computing [31] and for interacting condensate lattices [23, 32]. The latter are a very prospective platform for the development of simulator calculation approaches. There are numerous works demonstrating possibility to utilize the polariton condensate platform for solving some common numerical problems such as Max-three-cut [33], travelling salesman problem, Ising model [34], XY-Hamilto-nian [35].

Taking into account the fundamental and practical importance of structured light states and their prominent applications, the purpose of this thesis is an experimental and theoretical investigation of the properties of quantum vortices and the mechanisms of their formation in optically trapped exciton-polariton condensates.

In order to accomplish this goal, the tasks of this thesis are the following:

1. Implement the hologram calculation technique, for independent tuning of the parameters of the ring-shaped excitation beam (carrying orbital angular momentum (OAM), beam diameter, and ellipticity). Integrate this technique in the automation software of the experimental setup.

2. Find the parameters of non-resonant optical excitation for observation of vortex cluster formed in optically trapped polariton condensate due to the simultaneous occupation of two trapping potential manifolds.

3. Using interferometric methods, identify the spatial modes that correspond to the trap manifolds occupied by polaritons. Reconstruct the phase and intensity spatial distributions of these modes.

4. Build the experimental setup for the time-delayed interferometry of polariton photoluminescence with its expanded copy. Reconstruct the temporal dynamics of the beatings arising due to the presence of two energy-detuned spatial modes. Investigate the temporal dynamics of vortex clusters formed in optically trapped polariton condensate due to the simultaneous occupation of two trapping potential manifolds by implementing the time-delayed interferometry technique.

5. Find the excitation parameters for the observation of vortices and their clusters in the polariton condensates formed inside the rotating potentials. Implement the technique for synchronous control of the beams intensities that make up the rotating bichromatic beam.

6. Investigate the impact of rotating bichromatic beam parameters on the polariton condensate spectrum, the number of induced vortices, and the direction of their rotation.

Propositions for the defense:

1. Optically trapped polariton condensate occupying two energy levels corresponding to higher-order Ince-Gaussian modes IG^} and IG^l forms the cluster of vortices in the local minima of the polariton density. Energy (frequency) detuning between spatial modes leads to appearance of limit-cycle in the system and results in formation of vortices with periodically flipping topological charges. The charges flipping frequency is equal to the frequency difference between occupied states.

2. The frequency of oscillating topological charges appearing in the optically trapped polariton condensate occupying two energy levels corresponding to higher-order Ince-Gaussian modes IG^i and /G33 can be precisely tuned in the range of « 300 MHz by changing the ellipticity of the optical trap in the range from 0.95 up to 1.02;

3. The number of vortices emerged in the polariton condensate forming inside optically imprinted rotating potential by non-resonant bichromatic beam can be tuned in the range from 1 up to 4 by changing the excitation beam diameter, intensity, and rotation frequency; the number of emerged vortices is equal to the number n of dominantly occupied energy state; the direction of all single-charged vortices is determined and matches to the rotation direction of the externally induced potentials.

Scientific novelty:

1. The first experimental observation of the vortex cluster with periodically flipping topological charges spontaneously formed in the optically trapped polariton condensate occupying two energy levels corresponds to the higher-order Ince-Gaussian spatial modes. Spontaneous occupation of two energy levels leads to formation of cyclic temporal dynamics (limit cycle).

2. First time demonstrated the control on the flipping frequency of topologi-cal charges emerged in the trapped polariton condensate by changing the ellipticity of optically induced trapping potential.

3. The first experimental demonstration of the vortex cluster emergence in the trapped polariton condensate non-resonantly optically excited by bichro-matic rotating dumbbell shaped beam. The number of arising vortices in such system is determined by the energy level occupied by polariton condensate.

4. First time demonstrated the control of total carrying orbital angular momentum by changing the excitation power carrying by bichromatic rotating beam.

The theoretical and practical value of this research is the investigation of the new ways of control of the vorticity and its properties in optically trapped po-lariton condensates. The presented results open new prospective approaches for the fundamental investigation of Bose-Einstein condensation, superfluidity, and other physical phenomena that are accompanied by vorticity emerging. From the other

hand, investigation of vortices being a part of research field of singular optics potentially have some practical applications for optical communication lines, cryptography, optical tweezers etc.

Reliability. The credibility and repeatability of experimentally obtained results rely on well-proven experimental approaches and measurement techniques. The experimental setups are designed with the implementation of high-level modern equipment and components well aligned and set to each other. All experimentally obtained results are in good agreement with the theoretical calculations included in this thesis and with already published results from other scientific groups.

Work approbation. The materials of the work were presented in oral talks and discussed in 4 conferences:

A1. I. Gnusov, S. Harrison, S. Alyatkin, K. Sitnik, J. Topfer, H. Sigurdsson, P. Lagoudakis. "Quantized Vortex formation in the "Rotating bucket" Experiment with Nonlinear Fluids of Light". International Conference on Physics of Light-Matter Coupling in Nanostructures. Colombia, Medellin, 11-16 April 11-16, 2023.

A2. K.A. Sitnik, S.Y. Alyatkin, H. Siggurdson, J.D. Topfer, I.S. Gnusov, P.G. Lagoudakis. "Topological charges oscillations of quantum vortices cluster in optically trapped polariton condensate". All Russian conference with international participation Enysey's photonics. Russia, Krasnoyarsk, 19-23 September 2022.

A3. K.A. Sitnik, S. Alyatkin, J.D.Topfer, I. Gnusov, T. Cookson, H. Sigurdsson, P.G. Lagoudakis. "Temporal dynamics of flipping vortex cluster produced by beating Ince-Gaussian modes in trapped polariton condensate". International conference on laser physics and optics (ICLO). Russia, Saint-Petersburg, 20-24 June 2022.

A4. K.A. Sitnik, S. Alyatkin, H. Sigurdsson, and P. G. Lagoudakis, "Vortex crystals in optically trapped exciton-polariton condensates". International conference Frontiers in Optics and Laser Science (FIOLS). United States, Washington, DC (Online), 1-4 November 2021.

Publications. The results on the thesis topic are presented in 3 peer-reviewed Q1 papers indexed by Web of Science and Scopus data bases and in 1 international conference proceedings:

B1. K.A. Sitnik, I. Gnusov, M. Misko, J. D. Topfer, S. Alyatkin, P.G. Lagoudakis. "Control of the oscillation frequency of a vortex cluster in the trapped polariton condensate". In: Applied Physics Letters 124.20 (May 2024), pp.201102. DOI: 10.1063/5.0199548.

B2. I. Gnusov, S. Harrison, S. Alyatkin, K. Sitnik, H. Sigurdsson, P. G. Lagoudakis. "Vortex clusters in a stirred polariton condensate". In: Physical Review B 109.10 (Mar. 2024), pp.104503. DOI: 10.1103/Phys-RevB.109.104503.

B3. K. A. Sitnik, S. Alyatkin, J. D. Topfer, I. Gnusov, T. Cookson, H. Sigurdsson, P. G. Lagoudakis. "Spontaneous Formation of Time-Periodic Vortex Cluster in Nonlinear Fluids of Light". In: Physical Review Letters 128.23 (June 2022), pp.237402. DOI: 10.1103/PhysRevLett.128.237402.

B4. K. A. Sitnik, S. Alyatkin, H. Sigurdsson, P. G. Lagoudakis. "Vortex crystals in optically trapped exciton-polariton condensates". In: Frontiers in Optics + Laser Science (Nov. 2021), pp.JTh1A.1. DOI: 10.1364/FI0.2021.JTh1A.1. Personal contribution. The author personally took part in design of the experiments, building and alignment of the experimental setups, obtain the experimental results for B1, B3, B4 papers listed above. He takes part in the conducting of the experiments for B2 publication together with his colleague Ivan Gnusov. He provide post analysis for B1, B3, and B4 works. In addition he took part in theoretical calculations for B1 publication. He actively participated in discussion of scientific results, preparation of the manuscripts for all four works listed above.

The structure and volume of the thesis. The dissertation consists of an introduction, 4 chapters, and conclusion. It is written on 132 pages of typewritten text and includes 53 figures. The list of references includes 126 references titles.

Chapter 1 - Physics of planar microcavities contains description of the physical processes taking place inside the planar microcavity with embedded semiconductor quantum well, namely light-matter strong coupling, condensation of polaritons, superfluidity, optical trapping of polaritons and vortex formation;

Chapter 2 - Experimental methods and techniques is devoted to the detailed description of the experimental techniques which were used for obtaining of experimental data for this thesis. Besides, it also includes the de-

scription of calculation techniques that were implemented for the data analysis or beam shaping;

Chapter 3 - Charge-oscillating vortex cluster in this chapter we demonstrate the experimental results demonstrating optically trapped polari-ton condensate spontaneously arising and containing the vortex cluster with periodically flipping topological charges. The demonstrated experimental observations are corroborated by numerical simulations; Chapter 4 - Vortex clusters in optically induced rotational potentials is devoted to the observation of vortex cluster formation in the polariton condensate trapped in the rotating potential induced optically by using rotating bichromatic beam;

Conclusion final summary and discussion of the results of this work, their possible applications and possible ways of further research development.

Заключение диссертации по теме «Другие cпециальности», Ситник Кирилл Александрович

Conclusion

Photonics nowadays is blooming, studying not only the fundamental physical problems but aiming for practical applications. The achievements of the last several decades have led to the implementation of photonic devices in both industry (optical communication lines, laser material processing, etc.) and customers segments (quantum dot screens, LIDARs in smartphones, etc.). The integration of photonic technologies for data processing - analogue and neuromorphic computing is currently on the cutting edge of research. This activity now features numerous scientific reports and publications, even the first small scale productions and beta testing. We believe that polariton platform could make a significant contribution to the ongoing investigations and pursuits in this direction. In this thesis, we show that utilization of different trapping techniques allow for driving the condensate into exotic regimes and enables the control of different parameters of emerged vorticity.

To sum up, in Chapter 3 we demonstrate that polariton condensate spontaneously occupying two energy-split higher-order spatial modes demonstrating the limit cycle behavior, which presence was confidently demonstrates by experimental and theoretical approaches. The presence of duty cycle temporally modulates spatial distributions of the polariton density and phase and leads to formation of vortex clusters with topological charges periodically flipping with a GHz speed. Previously, that phenomenon had not been demonstrated in the polariton system, which undoubtedly will lead to new research proposals and possible applications of structured light. Moreover, using the control on ellipticity of optically induced trapping potential, we experimentally demonstrate the possibility of fine-tuning of the frequency topological charges flipping in the range of several hundred MHz. The demonstration of frequency control of topological charge flipping opens new ways for dynamic control of OAM, which previously was considered as a static degree of freedom of light waves.

Unlike the results demonstrated in Chapter 3 which deals with the spontaneous formation of vorticity in polariton condensates, Chapter 4 highlights the phenomenon of externally induced vorticity emergence. Using a bichromatic non-resonant annular rotating beam for optical trapping of polariton condensates, we demonstrate that fine tuning of the trapping parameters, such as the rotation

frequency, excitation power, and trap diameter, allows for the generation of vortex clusters with a controllable number of arising vortices. Moreover, all vortices in every demonstrated configuration co-rotate with the externally induced time periodic potentials. Therefore, the demonstrated trapping technique provides the full control over the arising vortex clusters.

The main results of this work are follows:

1. The first experimental observation of a vortex cluster with periodically oscillating topological charges in the trapped polariton condensate. It is demonstrated that the flipping of topological charges appears due to simultaneous occupation of two energy-detuned trap manifolds that correspond to the higher-order Ince-Gaussian modes IG31 and IG^. The experimentally demonstrated results are corroborated by the numerical simulations based on the 2DGPE equation.

2. The first experimental demonstration of the control of topological charge flipping frequency. It is demonstrated that scanning of the trap ellipticity in the range from 0.95 up to 1.02 allows to tune the topological charge flipping frequency in the range of « 300 MHz.

3. The first experimental observation of the externally induced formation of vortex clusters in the polariton condensate arising in the rotating potential. The control of the emerged vortices number from one up to four is demonstrated.

4. It is demonstrated the regime that allows to switch the polariton condensate between three rotating trap manifolds: 2nd excited, 1st excited and the ground state by tuning only the excitation power. Moreover, switching between energy levels is implemented for tuning the total OAM carried by trapped polariton condensate between 0, 1, and 2.

Список литературы диссертационного исследования кандидат наук Ситник Кирилл Александрович, 2024 год

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Other author's publication not included in this thesis

1. S. Alyatkin, H. Sigursson, Y. V. Kartashov, I. Gnusov, K. Sitnik, J. D. Topfer, P. G. Lagoudakis. "All-optical triangular and honeycomb lattices of exciton-polaritons". In: Applied Physics Letters 124.6 (Jan. 2024), p. 062105. DOI: 10.1063/5.0180272.

2. I. Gnusov, S. Harrison, S. Alyatkin, K. Sitnik, J. Topfer, H. Sigurdsson, P. Lagoudakis. "Quantum vortex formation in the "rotating bucket" experiment with polariton condensates". In: Science Advances 9.4 (Jan. 2023). p. eadd1299. DOI: 10.1126/sciadv.add1299.

3. S. Alyatkin, C. Milian, Y. V. Kartashov, K. A. Sitnik, J. D. Topfer, H. Sigurdsson, P. G. Lagoudakis. "All-optical artificial vortex matter in quantum fluids of light". In: arXiv (July 2023). DOI: 10.48550/arXiv.2207.01850.

4. A. A. Mkrtchyan, Y. G. Gladush, M. A. Melkumov, A. M. Khegai, K. A Sitnik, P. G. Lagoudakis, A. G. Nasibulin. "Nd-doped polarization maintaining all-fiber laser with dissipative soliton resonance mode-locking at 905 nm". In: Journal of Lightwave Technology 39.17 (Sep. 2023), pp. 5582-5588. DOI: 10.1109/JLT.2021.3085538.

5. N. G. Ivanov, V. F. Losev, V. E. Prokop'ev, K. A. Sitnik, I. A. Zyatikov, "High time-resolved spectroscopy of filament plasma in air". In: Optics Communications 431 (Mar. 2017), pp. 120-125. DOI: 10.1016/j.optcom.2018.09.007.

6. N. G. Ivanov, V. F. Losev, V. E. Prokop'ev, K. A. Sitnik. "Generation of a highly directional supercontinuum in the visible spectrum range". In: Science Advances 387 (Mar. 2017), pp.322-327. DOI: 10.1016/j.optcom.2016.11.057.

7. N. G. Ivanov, V. F. Losev, V. E. Prokop'ev, K. A. Sitnik. "Superradiance by molecular nitrogen ions in filaments". In: Atmospheric and Oceanic Optics 29. (Jul. 2016), pp.385-389. DOI: 10.1134/S1024856016040072.

8. V. P. Demkin, H Kingma, R. Van De Berg, S. V. Melnichuk, O. V. Demkin, M-S Herards, V. S. Ripenko, K. A. Sitnik. "Determination of the electrophysical parameters of a beam-type high-voltage pulsed discharge

plasma for biomedical research in a highly efficient computing environment". In: Russian Physics Journal 58.5 (Sep. 2015), pp. 740-744. DOI: 10.1007/s11182-015-0560-3.