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  • 1. Banerjee, R.
    et al.
    Liew, T. C. H.
    Kyriienko, Oleksandr
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Realization of Hofstadter's butterfly and a one-way edge mode in a polaritonic system2018In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 98, no 7, article id 075412Article in journal (Refereed)
    Abstract [en]

    We present a scheme to generate an artificial gauge field for the system of neutral bosons, represented by polaritons in micropillars arranged into a square lattice. The splitting between the two polarizations of the micropillars breaks the time-reversal symmetry (TRS) and results in the effective phase-dependent hopping between cavities. This can allow for engineering a nonzero flux on the plaquette, corresponding to an artificial magnetic field. Changing the phase, we observe a characteristic Hofstadter's butterfly pattern and the appearance of chiral edge states for a finite-size structure. For long-lived polaritons, we show that the propagation of wave packets at the edge is robust against disorder. Moreover, given the inherent driven-dissipative nature of polariton lattices, we find that the system can exhibit topological lasing, recently discovered for active ring cavity arrays. The results point to a static way to realize artificial magnetic field in neutral spinful systems, avoiding the periodic modulation of the parameters or strong spin-orbit interaction. Ultimately, the described system can allow for high-power topological single-mode lasing which is robust to imperfections.

  • 2. Dellantonio, Luca
    et al.
    Kyriienko, Oleksandr
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Copenhagen, Denmark.
    Marquardt, Florian
    Sørensen, Anders S.
    Quantum nondemolition measurement of mechanical motion quanta2018In: Nature Communications, ISSN 2041-1723, E-ISSN 2041-1723, Vol. 9, article id 3621Article in journal (Refereed)
    Abstract [en]

    The fields of optomechanics and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical motion and the associated quantum jumps between phonon states remains elusive. For optomechanical systems, the coupling to the environment was shown to make the detection of the mechanical mode occupation difficult, typically requiring the single-photon strong coupling regime. Here, we propose and analyse an electromechanical setup, which allows us to overcome this limitation and resolve the energy levels of a mechanical oscillator. We found that the heating of the membrane, caused by the interaction with the environment and unwanted couplings, can be suppressed for carefully designed electromechanical systems. The results suggest that phonon number measurement is within reach for modern electromechanical setups.

  • 3. Kibis, O.
    et al.
    Kyriienko, Oleksandr
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). ITMO University, Russia.
    Shelykh, I. A.
    Structure of surface electronic states in strained mercury telluride2019In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 21, article id 043016Article in journal (Refereed)
    Abstract [en]

    We present the theory describing the various surface electronic states arisen from the mixing of conduction and valence bands in a strained mercury telluride (HgTe) bulk material. We demonstrate that the strain-induced band gap in the Brillouin zone center of HgTe results in the surface states of two different kinds. Surface states of the first kind exist in the small region of electron wave vectors near the center of the Brillouin zone and have the Dirac linear electron dispersion characteristic for topological states. The surface states of the second kind exist only far from the center of the Brillouin zone and have the parabolic dispersion for large wave vectors. The structure of these surface electronic states is studied both analytically and numerically in the broad range of their parameters, aiming to develop its systematic understanding for the relevant model Hamiltonian. The results bring attention to the rich surface physics relevant for topological systems.

  • 4. Kibis, O.
    et al.
    Kyriienko, Oleksandr
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Shelykh, I. A.
    Topological Electronic States on the Surface of a Strained Gapless Semiconductor2019In: Semiconductors (Woodbury, N.Y.), ISSN 1063-7826, E-ISSN 1090-6479, Vol. 53, no 14, p. 1867-1869Article in journal (Refereed)
    Abstract [en]

    We develop the theory describing the topological electronic states on the surface of a gapless strained semiconductor arisen from the mixing of conduction and valence bands. It follows from the present theory that the strain-induced band gap in the Brillouin zone center of the semiconductor results in the surface electronic states with the Dirac linear dispersion characteristic for topologically protected states. The structure of these surface electronic states is studied analytically near their Dirac point within the formalism based on the Luttinger Hamiltonian. The results bring attention to the rich surface physics relevant for topological systems.

  • 5. Kozin, Valerii K.
    et al.
    Kyriienko, Oleksandr
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Exeter, United Kingdom; ITMO University, Russia.
    Quantum Time Crystals from Hamiltonians with Long-Range Interactions2019In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 123, no 21, article id 210602Article in journal (Refereed)
    Abstract [en]

    Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where an external drive allows us to break discrete TTS, ultimately leading to Floquet time crystals. At the same time, genuine time crystals for closed quantum systems are believed to be impossible. In this study we propose a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS. This is based on a spin-1/2 many-body Hamiltonian which has long-range multispin interactions in the form of spin strings, thus bypassing previously known no-go theorems. We show that quantum time crystals are stable to local perturbations at zero temperature. Finally, we reveal the intrinsic connection between continuous and discrete TTS, thus linking the two realms.

  • 6.
    Kyriienko, Oleksandr
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Exeter, UK; ITMO University, Russia.
    Quantum inverse iteration algorithm for programmable quantum simulators2020In: npj Quantum Information, E-ISSN 2056-6387, Vol. 6, no 1, article id 7Article in journal (Refereed)
    Abstract [en]

    We propose a quantum inverse iteration algorithm, which can be used to estimate ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the Hamiltonian inverse to an initial state prepares the approximate ground state. To apply the inverse Hamiltonian operation, we write it as a sum of unitary evolution operators using the Fourier approximation approach. This allows to reformulate the protocol as separate measurements for the overlap of initial and propagated wavefunction. The algorithm thus crucially depends on the ability to run Hamiltonian dynamics with an available quantum device, and can be used for analog quantum simulators. We benchmark the performance using paradigmatic examples of quantum chemistry, corresponding to molecular hydrogen and beryllium hydride. Finally, we show its use for studying the ground state properties of relevant material science models, which can be simulated with existing devices, considering an example of the Bose-Hubbard atomic simulator.

  • 7.
    Kyriienko, Oleksandr
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). ITMO University, Russia.
    Kibis, O.
    Shelykh, I. A.
    Optically induced topological states on the surface of mercury telluride2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 11, article id 115411Article in journal (Refereed)
    Abstract [en]

    We developed the theory which describes the Floquet engineering of surface electronic modes in bulk mercury telluride (HgTe) by a circularly polarized electromagnetic field. The analysis shows that the field results in the appearance of the surface states which arise from the mixing of conduction and valence bands of HgTe. Their branches lie near the center of the Brillouin zone and have the Dirac dispersion characteristic for topological states. Besides them, the irradiation induces the gap between the conduction and valence bands of HgTe. Thus, the irradiation can turn mercury telluride into a topological insulator from a gapless semiconductor. It is demonstrated that the optically induced states differ substantially from the nontopological surface states existing in HgTe without irradiation. The structure of the found states is studied both analytically and numerically in the broad range of their parameters.

  • 8.
    Kyriienko, Oleksandr
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). ITMO University, Russia.
    Sigurdsson, H.
    Liew, T. C. H.
    Probabilistic solving of NP-hard problems with bistable nonlinear optical networks2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 19, article id 195301Article in journal (Refereed)
    Abstract [en]

    We study theoretically a lattice of locally bistable driven-dissipative nonlinear cavities. The system is found to resemble the classical Ising model and enables its effective simulation. First, we benchmark the performance of driven-dissipative nonlinear cavities for spin-glass problems, and study the scaling of the ground-state-energy deviation and success probability as a function of system size. Next, we show how an effective bias field can be included in an optical model and use it for probabilistic solving of optimization problems. As particular examples we consider NP-hard problems embedded in the Ising model, namely graph partitioning and the knapsack problem. Finally, we confirm that locally bistable polariton networks act as classical optimizers and can potentially provide an improvement within the exponential complexity class.

  • 9. Shahnazaryan, V.
    et al.
    Kyriienko, Oleksandr
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). ITMO University, Russia; University of Exeter, United Kingdom.
    Rostami, Habib
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Exciton routing in the heterostructure of a transition metal dichalcogenide monolayer on a paraelectric substrate2019In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 100, no 16, article id 165303Article in journal (Refereed)
    Abstract [en]

    We propose a scheme for the spatial exciton energy control and exciton routing in a transition-metal dichalcogenide (TMD) monolayer which lies on a quantum paraelectric substrate. It relies on the ultrasensitive response of the substrate dielectric permittivity to temperature changes, allowing for spatially inhomogeneous screening of Coulomb interaction in a monolayer. As an example, we consider the heterostructure of TMD and strontium titanate oxide SrTiO3, where large dielectric screening can be attained. We study the impact of substrate temperature on the characteristic electronic features of TMD monolayers such as the particle band gap and exciton binding energy, Bohr radius, and nonlinearity (an exciton-exciton interaction). The combination of particle band gap and exciton binding energy modulation results in the shift of the exciton resonance energy. Applying local heating, we create spatial patterns with varying exciton resonant energy and an exciton flow toward the energetically lower region of the sample.

  • 10. Sigurdsson, Helgi
    et al.
    Kyriienko, Oleksandr
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Dini, Kevin
    Liew, Timothy C. H.
    All-to-All Intramodal Condensate Coupling by Multifrequency Excitation of Polaritons2019In: ACS Photonics, E-ISSN 2330-4022, Vol. 6, no 1, p. 123-129Article in journal (Refereed)
    Abstract [en]

    We analyze theoretically a network of all-to-all coupled polariton modes, realized by a trapped polariton condensate excited by a multifrequency laser source. In the low-density regime the system dynamically finds a state with maximal gain defined by the average intensities (weights) of the different source frequency components, analogous to active mode locking in lasers, and thus solves a maximum eigenvalue problem set by the matrix of weights. The method opens the possibility to tailor condensed polariton populations in different trapped modes by appropriate choice of the excitation source.

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