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arXiv:1907.00383 · Physical Review Research

Split-ring polariton condensates as macroscopic two-level quantum systems

Yan Xue, Igor Yu. Chestnov, Evgeny Sedov, Evgeniy O. Kiktenko, Aleksey K. Fedorov, Stefan Schumacher, Xuekai Ma, Alexey Vitalievich Kavokin

Published Jan 29, 2021• 60 citations
arXivHTMLPDF

Abstract

Superposition states of circular currents of exciton-polaritons mimic the superconducting flux qubits.The phase of a polariton fluid must change by an integer number of 2π when going around the ring.If one introduces a π -phase delay line in the ring, the fluid is obliged to propagate a clockwise or anticlockwise circular current to reduce the total phase gained over one round trip to zero or to build it up to 2π .We show that such a π -delay line can be provided by a dark soliton pinned to a potential well created by a C-shape nonresonant pump spot.The resulting split-ring polariton condensates exhibit pronounced coherent oscillations passing periodically through clockwise and anticlockwise current states.These oscillations may persist far beyond the coherence time of polariton condensates.The qubits based on split-ring polariton condensates are expected to possess very high figures of merit that makes them a valuable alternative to superconducting qubits.The use of the dipole-polarized polaritons allows one to control coherently the state of the qubit with the external electric field.This is shown to be one of the tools for realization of single-qubit logic operations.We propose the design of an iSWAP gate based on a pair of coupled polariton qubits.To demonstrate the capacity of the polariton platform for quantum computations, we propose a protocol for the realization of Deutsch's algorithm with polariton qubit networks.

DOI
10.1103/physrevresearch.3.013099

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Superposition states of circular currents of exciton-polaritons mimic the superconducting flux qubits.The phase of a polariton fluid must change by an integer number of 2π when going around the ring.If one introduces a π -phase delay line in the ring, the fluid is obliged to propagate a clockwise or anticlockwise circular current to reduce the total phase gained over one round trip to zero or to build it up to 2π .We show that such a π -delay line can be provided by a dark soliton pinned to a potential well created by a C-shape nonresonant pump spot.The resulting split-ring polariton condensates exhibit pronounced coherent oscillations passing periodically through clockwise and anticlockwise current states.These oscillations may persist far beyond the coherence time of polariton condensates.The qubits based on split-ring polariton condensates are expected to possess very high figures of merit that makes them a valuable alternative to superconducting qubits.The use of the dipole-polarized polaritons allows one to control coherently the state of the qubit with the external electric field.This is shown to be one of the tools for realization of single-qubit logic operations.We propose the design of an iSWAP gate based on a pair of coupled polariton qubits.To demonstrate the capacity of the polariton platform for quantum computations, we propose a protocol for the realization of Deutsch's algorithm with polariton qubit networks.
Superposition states of circular currents of exciton-polaritons mimic the superconducting flux qubits. The current states are formed by a macroscopic number of bosonic quasiparticles that compose a single quantum state of a many-body condensate. The essential difference between a polariton fluid and a supercurrent comes from the fact that polaritons are electrically neutral, and the magnetic field would not have a significant effect on a polariton current. Nevertheless, the phase of a polariton condensate must change by an integer number of 2π2\pi2π, when going around the ring. If one introduces a π\piπ-phase delay line in the ring, the system is obliged to propagate a clockwise or anticlockwise circular current to reduce the total phase gained over one round-trip to zero or to build it up to 2π2\pi2π. We show that such a π\piπ-delay line can be provided by a dark soliton embedded into a ring condensate and pinned to a potential well created by the C-shape non-resonant pump-spot. The physics of resulting split-ring polariton condensates is essentially similar to the physics of flux qubits. In particular, they exhibit pronounced coherent oscillations passing periodically through clockwise and anticlockwise current states. We predict that these oscillations should persist far beyond the coherence time of the polariton condensates. As a consequence the qubits based on split-ring polariton condensates are expected to be characterized by a very high figure of merit that makes them a valuable alternative to superconducting qubits.
Recently, split-ring bosonic condensates of exciton polaritons have been proposed for realisation of qubits. We formulate an analytical model of a polariton condensate in a one-dimensional ring split by a delta-function potential. The persistent current is stopped by the potential defect embedded in a scalar condensate of non-interacting particles, however, it reappears in the presence of an up-critical non-linearity. The nonlinear supercurrents are characterised by fractional orbital momenta while their eigenfunctions may feature grey or dark solitons. The coupling between the spin and the orbital angular momentum of a spinor condensate affects persistent currents crucially. We show that the spin-orbit interaction (SOI) induces the net superfluid current in the condensate with a spatially uniform spin polarisation. We also find solutions where the SOI-induced currents of two spin components of the condensate propagate in opposite directions. The corresponding states of spinor condensates obey a combined mirror reflection and the spin-flip symmetry.
Bosonic condensates of spinless noninteracting particles confined on a ring cannot propagate circular periodic currents once rotation symmetry of the system is broken. However, a persistent current may appear due to interparticle interactions exceeding some critical strength. In this up-critical regime breaking of the symmetry between the clockwise and anticlockwise rotations takes place. We consider this symmetry-breaking scenario in the case of a spinor condensate of exciton polaritons trapped on a ring split by a potential barrier. Due to the intrinsic symmetry of the effective spin-orbit interaction, which stems from the linear splitting between transverse-electric and transverse-magnetic microcavity modes, the potential barrier blocks the circulating current and imposes linear polarization patterns. On the other hand, circularly polarized polaritons form circular currents propagating in opposite directions with equal absolute values of angular momentum. In the presence of interparticle interactions, the symmetry of clockwise and anticlockwise currents can be broken spontaneously. We describe several symmetry-breaking scenarios, which imply either restoration of the global condensate rotation or the onset of the circular polarization in the symmetry-broken state.
We create exciton–polariton condensates in half-moon shapes by the nonresonant optical excitation of GaAs-based cylindrical pillar microcavities. In this geometry, the π-jump of the phase of the condensate wave function coexists with a gradual ±π phase variation between two horns of the half-moon. We switch between clockwise and counterclockwise phase currents by slightly shifting the excitation spot on the surface of the pillar. Half-moon condensates are expected to reveal features of two-level quantum systems similar to superconducting flux qubits.
We predict the spontaneous symmetry breaking in a spinor Bose-Einstein condensate of exciton-polaritons (polaritons) caused by the coupling of its spin and orbital degrees of freedom. We study a polariton condensate trapped in a ring-shaped effective potential with a broken rotational symmetry. We propose a realistic scheme of generating controllable spinor azimuthal persistent currents of polaritons in the trap under the continuous wave optical pump. We propose a new type of half-quantum circulating states in a spinor system characterized by azimuthal currents in both circular polarizations and a vortex in only one of the polarizations. The spontaneous symmetry breaking in the spinor polariton condensate that consists in the switching from co-winding to opposite-winding currents in opposite spin states is revealed. It is characterized by the change of the average orbital angular momentum of the condensate from zero to non-zero values. The radial displacement of the pump spot and the polarization of the pump act as the control parameters. The considered system exhibits a fundamental similarity to a superconducting flux qubit, which makes it highly promising for applications in quantum computing.
We report the observation of coherent circulation in a macroscopic Bose-Einstein condensate of polaritons in a ring geometry. Because they are spinor condensates, half-quanta are allowed in where there is a phase rotation of π in connection with a polarization vector rotation of π around a closed path. This half-quantum behavior is clearly seen in the experimental observations of the polarization rotation around the ring. In our ring geometry, the half-quantum state that we see is one in which the handedness of the spin flips from one side of the ring to the other side in addition to the rotation of the linear polarization component; such a state is allowed in a ring geometry but will not occur in a simply connected geometry. This state is lower in energy than a half-quantum state with no change of the spin direction and corresponds to a superposition of two different elementary half-quantum states. The direction of circulation of the flow around the ring fluctuates randomly between clockwise and counterclockwise from one shot to the next; this fluctuation corresponds to spontaneous breaking of time-reversal symmetry in the system. This type of macroscopic polariton ring condensate allows for the possibility of direct control of the circulation to excite higher quantized states and the creation of Josephson junction tunneling barriers.