Stochastic circular persistent currents of exciton polaritons J. Borat12 Roman Cherbunin3 Evgeny Sedov1234 Ekaterina Aladinskaia3 Alexey Liubomirov3 Valentina Litvyak3 Mikhail Petrov3 Xiaoqing Zhou12 Z. Hatzopoulos5

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Stochastic circular persistent currents of exciton polaritons

J. Borat1,2, Roman Cherbunin3, Evgeny Sedov1,2,3,4,∗, Ekaterina Aladinskaia3,

Alexey Liubomirov3, Valentina Litvyak3, Mikhail Petrov3, Xiaoqing Zhou1,2, Z. Hatzopoulos5,

Alexey Kavokin1,2,4,6, P. G. Savvidis1,2,5,7

1Key Laboratory for Quantum Materials of Zhejiang Province, School of Science, Westlake University, 18 Shilongshan

Rd, Hangzhou 310024, Zhejiang, China

2Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou, Zhejiang

Province 310024, China

3Spin Optics Laboratory, St. Petersburg State University, Ulyanovskaya 1, St. Petersburg 198504, Russia

4Vladimir State University named after A. G. and N. G. Stoletovs, Gorky str. 87, Vladimir 600000, Russia

5FORTH-IESL, P.O. Box 1527, 71110 Heraklion, Crete, Greece

6Moscow Institute of Physics and Technology, Institutskiy per., 9, Dolgoprudnyi, Moscow Region, 141701, Russia

7Department of Materials Science and Technology, University of Crete, P.O. Box 2208, 71003 Heraklion, Crete, Greece

*evgeny_sedov@mail.ru

October 12, 2022

Abstract

We keep track of the orbital degree of freedom of an exciton polariton condensate, conﬁned in an optical

trap, and reveal the stochastic switching of persistent annular polariton currents in the pulse-periodic excita-

tion regime. In an elliptic trap, the low-lying in energy polariton current states are inherent in a two-petalled

density distribution and swirling phase. In the stochastic regime, the averaged over multiple excitation pulses

density distribution gets homogenised in the azimuthal direction, while the weighted phase extracted from

interference experiments experiences two compensating each other jumps, when varying around the center

of the trap. Breaking the reciprocity of the system with a supplemental control optical pulse makes it pos-

sible to switch the system from the stochastic regime to the deterministic regime of an arbitrary polariton

circulation.

Introduction

Recently, much attention in polaritonics has been given to the orbital degree of freedom. Exciton polaritons,

eigenmodes of optical microcavities strongly coupled to excitons in embedded semiconductor quantum wells

(QWs) [1], form macroscopic states of exciton-polariton condensates that behave like a superﬂuid liquid [2,3].

Flows of polaritons within the condensate state endow the latter with the nonzero orbital angular momentum

(OAM). Polariton condensates in annular [4–7] and pot-shaped [8,9] traps, traps of complicated shape [10,11],

trap chains and clusters [12–14] have been considered for the study of and manipulation by their OAM. Such

attention to this problem is justiﬁed by the broad prospects for the use of orbital degree of freedom for quantum

and classical information storage and processing [15–18] as well as for optical communications [19,20].

Polariton vortices are the most prominent representatives of polariton condensate states with nonzero OAM.

The spontaneous formation of polariton vortices (in the form of vortex-antivortex pairs and clusters) has been

extensively studied [21–23]. A separate area of research is the excitation of vortices with predeﬁned OAM (or,

equivalently, the direction and distribution of the polariton ﬂow density). Among the used approaches are

the resonant excitation scheme and resonant imprinting of OAM [24–26], engineering of the eﬀective complex

trapping potential [4–6,10] under the incoherent excitation, and the ill-understood direct transfer of OAM from

the non-resonant optical pump beam [27]. Incoherent control of polariton vortices was reported in [28] for

short-lived polaritons characterized by a lifetime of units of picoseconds. Such polaritons are unable to undergo

long-range ballistic behavior. They form macroscopic coherent states predominantly under the pump spot, so

the gain-induced trapping is realized for such polaritons [18,29,30].

In our paper, we study both experimentally and numerically formation of persistent polariton currents in an

optically induced elliptical pot-shaped trap created in a planar microcavity. In the experiment, we demonstrate

arXiv:2210.05299v1 [cond-mat.mes-hall] 11 Oct 2022

Substrate

Cavity

layer

QWs

Non-resonant

Control pump

Photoluminescence

(a) (b)

(c)

pump



Figure 1: (Color online) (a) Schematic of excitation of the polariton condensate with a nonresonant annular

optical pump in a planar microcavity with embedded quantum wells. Luminescence of the sample under the

non-resonant optical pump below the polariton condensation threshold in the absence (b) and in the presence

controllable non-resonant excitation of polariton condensates supporting internal persistent polariton ﬂows.

Their two-petal shape, contrary to expectation, does not indicate the formation of a phase-locked standing

wave (see, e.g., [31,32]), but coexists with its phase, swirling around the center of the trap. We demonstrate

the stochastic switching between two orthogonal polariton current states under the pulse-periodic nonresonant

optical excitation.

Polariton currents resulting in nonzero OAM of the polariton condensate are reﬂected in a twisted wavefront

of its photoluminescence (PL), which makes it possible to judge the polariton ﬂows from the phase distribution

of PL. To reveal circulation of the polariton condensate phase, we use the interferometry measurements [4,5].We

use the Mach-Zehnder interferometer with the spherical reference wave.

Results

Experiment

Schematically the creation of a polariton condensate is illustrated in Fig. 1(a). The condensate is created in

planar optical microcavity with embedded quantum wells by the nonresonant (at the upper Bragg mode of the

microcavity) optical pump of annular shape (with radius of about 19 µm) with a weak ellipticity in the pulse-

periodic regime with pulse duration of 1 ps and interpulse interval of 13 ns. See details of the sample under the

study in Methods. Figure 1(b) shows luminescence from the sample at the pump power considerably below the

polariton condensation threshold, which gives an idea of the shape of the pump. Pumping creates a reservoir of

incoherent excitons, which spatial distribution replicates the shape of the pump. The reservoir acts as a source

of polaritons for the condensate feeding it via stimulated relaxation processes. At the same time, due to the

repulsive polariton-exciton interaction, the reservoir plays a role of the trapping potential for polaritons. The

emerging polaritons in the structure live long enough (with lifetime estimated as tens of picoseconds) to go down

the potential hill to the bottom of the trap and occupy eigenstates of the trap. Due to the dissipative nature of

polaritons and to the presence of the pumping, the occupied eigenstate does not have to be the ground state of

the trap, but the state with the most advantageous balance of distributed in the microcavity plane losses and

gain [33,34]. The latter is determined by the overlapping of the polariton condensate wave function and the

cloud of the reservoir excitons.

In the ﬁrst experiment, we optically excite the polariton condensate and detect its PL spatial distribution,

averaged in time, see Fig. 2(a). The polariton condensate has a closed, close to annular shape weakly modulated

in the azimuthal direction. We observe interference of the condensate PL with a spherical reference wave, see

the interferometry image in Fig. 2(b). The coherent spherical wave was obtained by magnifying the part of

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摘要：

StochasticcircularpersistentcurrentsofexcitonpolaritonsJ.Borat1;2,RomanCherbunin3,EvgenySedov1;2;3;4;,EkaterinaAladinskaia3,AlexeyLiubomirov3,ValentinaLitvyak3,MikhailPetrov3,XiaoqingZhou1;2,Z.Hatzopoulos5,AlexeyKavokin1;2;4;6,P.G.Savvidis1;2;5;71KeyLaboratoryforQuantumMaterialsofZhejiangProvince,S...

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Stochastic circular persistent currents of exciton polaritons J. Borat12 Roman Cherbunin3 Evgeny Sedov1234 Ekaterina Aladinskaia3 Alexey Liubomirov3 Valentina Litvyak3 Mikhail Petrov3 Xiaoqing Zhou12 Z. Hatzopoulos5

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