Quantum dynamics of disordered arrays of interacting superconducting qubits: signatures of quantum collective states

  1. M. V. Fistul,
  2. O. Neyenhuys,
  3. A. B. Bocaz,
  4. and I. M. Eremin
We study theoretically the collective quantum dynamics occurring in various interacting superconducting qubits arrays (SQAs) in the presence of a spread of individual qubit frequencies.
The interaction is provided by mutual inductive coupling between adjacent qubits (short-range Ising interaction) or inductive coupling to a low-dissipative resonator (long-range exchange interaction). In the absence of interaction the Fourier transform of temporal correlation function of the total polarization (z-projection of the total spin), i.e. the dynamic susceptibility C(ω), demonstrates a set of sharp small magnitude resonances corresponding to the transitions of individual superconducting qubits. We show that even a weak interaction between qubits can overcome the disorder with a simultaneous formation of the collective excited states. This collective behavior manifests itself by a single large resonance in C(ω). In the presence of a weak non-resonant microwave photon field in the low-dissipative resonator, the positions of dominant resonances depend on the number of photons, i.e. the collective ac Stark effect. Coupling of an SQA to the transmission line allows a straightforward experimental access of the collective states in microwave transmission experiments and, at the same time, to employ SQAs as sensitive single-photon detectors.

Quantum beats of a magnetic fluxon in a two-cell SQUID

  1. I. N. Moskalenko,
  2. I. S. Besedin,
  3. S. S. Seidov,
  4. M. V. Fistul,
  5. and A. V. Ustinov
We report a detailed theoretical study of a coherent macroscopic quantum-mechanical phenomenon – quantum beats of a single magnetic fluxon trapped in a two-cell SQUID of high
kinetic inductance. We calculate numerically and analytically the low-lying energy levels of the fluxon, and explore their dependence on externally applied magnetic fields. The quantum dynamics of the fluxon shows quantum beats originating from its coherent quantum tunneling between the SQUID cells. We analyze the experimental setup based on a three-cell SQUID, allowing for time-resolved measurements of quantum beats of the fluxon.

Time molecules with periodically driven interacting qubits

  1. K. V. Shulga,
  2. I. Vakulchyk,
  3. Y. Nakamura,
  4. S. Flach,
  5. and M. V. Fistul
We provide numerical evidence for a temporal quantum-mechanical interference phenomenon: time molecules (TM). A variety of such stroboscopic states are observed in the dynamics of two
interacting qubits subject to a periodic sequence of π-pulses with the period T. The TMs appear periodically in time and have a large duration, δtTM≫T. All TMs demonstrate an almost zero value of the total polarization and a strong enhancement of the entanglement entropy S up to the maximum value S=ln2 of a corresponding Bell state. The TMs are generated by the commensurability of the Floquet eigenvalues and the presence of maximally entangled Floquet eigenstates. The TMs remain stable with detuned system parameters and with an increased number of qubits. The TMs can be observed in microwave experiments with an array of superconducting qubits.

Circuit Quantum Electrodynamics of Granular Aluminum Resonators

  1. N. Maleeva,
  2. L. Grünhaupt,
  3. T. Klein,
  4. F. Levy-Bertrand,
  5. O. Dupré,
  6. M. Calvo,
  7. F. Valenti,
  8. P. Winkel,
  9. F. Friedrich,
  10. W. Wernsdorfer,
  11. A. V. Ustinov,
  12. H. Rotzinger,
  13. A. Monfardini,
  14. M. V. Fistul,
  15. and I. M. Pop
The introduction of crystalline defects or dopants can give rise to so-called „dirty superconductors“, characterized by reduced coherence length and quasiparticle mean free
path. In particular, granular superconductors such as Granular Aluminum (GrAl), consisting of remarkably uniform grains connected by Josephson contacts have attracted interest since the sixties thanks to their rich phase diagram and practical advantages, like increased critical temperature, critical field, and kinetic inductance. Here we report the measurement and modeling of circuit quantum electrodynamics properties of GrAl microwave resonators in a wide frequency range, up to the spectral superconducting gap. Interestingly, we observe self-Kerr coefficients ranging from 10−2 Hz to 105 Hz, within an order of magnitude from analytic calculations based on GrAl microstructure. This amenable nonlinearity, combined with the relatively high quality factors in the 105 range, open new avenues for applications in quantum information processing and kinetic inductance detectors.

Double resonance response of a superconducting quantum metamaterial: manifestation of non-classical states of photons

  1. M. A. Iontsev,
  2. S. I. Mukhin,
  3. and M. V. Fistul
We report a theoretical study of ac response of superconducting quantum metamaterials (SQMs), i.e. an array of qubits (two-levels system) embedded in the low-dissipative resonator.
By making use of a particular example of SQM, namely the array of charge qubits capacitively coupled to the resonator, we obtain a second-order phase transition between an incoherent (the high-temperature phase) and coherent (the low-temperatures phase) states of photons. This phase transition in many aspects resembles the paramagnetic-ferromagnetic phase transition. The critical temperature of the phase transition, T⋆, is determined by the energy splitting of two-level systems δ, number of qubits in the array N, and the strength of the interaction η between qubits and photons in the cavity. We obtain that the photon states manifest themselves by resonant drops in the frequency dependent transmission D(ω) of electromagnetic waves propagating through a transmission line weakly coupled to the SQM. At high temperatures the D(ω) displays a single resonant drop, and at low temperatures a peculiar \emph{double resonance response} has to be observed. The physical origin of such a resonant splitting is the quantum oscillations between two coherent states of photons of different polarizations.

Generation of non-classical photon states in superconducting quantum metamaterials

  1. S. I. Mukhin,
  2. and M. V. Fistul
We report a theoretical study of diverse non-classical photon states that can be realized in superconducting quantum metamaterials. As a particular example of superconducting quantum
metamaterials an array of SQUIDs incorporated in a low-dissipative transmission line (resonant cavity) will be studied. This system will be modeled as a set of two-levels systems (qubits) strongly interacting with resonant cavity photons. We predict and analyze {a second(first)-order phase transition} between an incoherent (the high-temperature phase) and coherent (the low-temperatures phase) states of photons. In equilibrium state the partition function $Z$ of the electromagnetic field (EF) in the cavity is determined by the effective action $S_{eff}{P(tau)}$ that, in turn, depends on imaginary-time dependent momentum of photon field $P(tau)$. We show that the order parameter of this phase transition is the $P_{0}(tau)$ minimizing the effective action of a whole system. In the incoherent state the order parameter $P_{0}(tau)=0$ but at low temperatures we obtain various coherent states characterized by non-zero values of $P_{0}(tau)$. This phase transition in many aspects resembles the Peierls metal-insulator and the metal-superconductor phase transitions. The critical temperature of such phase transition $T^star$ is determined by the energy splitting of two-level systems $Delta$, a number of SQUIDs in the array $N$, and the strength of the interaction $eta$ between SQUIDs and photons in cavity.