New class of quantum error-correcting codes for a bosonic mode

We construct a new class of quantum error-correcting codes for a bosonic mode which are advantageous for applications in quantum memories, communication, and scalable computation. These 'binomial quantum codes' are formed from a finite superposition of Fock states weighted with binomial coefficients. The binomial codes can exactly correct errors that are polynomial up to a specific degree in bosonic creation and annihilation operators, including amplitude damping and displacement noise as well as boson addition and dephasing errors. For realistic continuous-time dissipative evolution, the codes can perform approximate quantum error correction to any given order in the timestep between error detection measurements. We present an explicit approximate quantum error recovery operation based on projective measurements and unitary operations. The binomial codes are tailored for detecting boson loss and gain errors by means of measurements of the generalized number parity. We discuss optimization of the binomial codes and demonstrate that by relaxing the parity structure, codes with even lower unrecoverable error rates can be achieved. The binomial codes are related to existing two-mode bosonic codes but offer the advantage of requiring only a single bosonic mode to correct amplitude damping as well as the ability to correct other errors. Our codes are similar in spirit to 'cat codes' based on superpositions of the coherent states, but offer several advantages such as smaller mean number, exact rather than approximate orthonormality of the code words, and an explicit unitary operation for repumping energy into the bosonic mode. The binomial quantum codes are realizable with current superconducting circuit technology and they should prove useful in other quantum technologies, including bosonic quantum memories, photonic quantum communication, and optical-to-microwave up- and down-conversion.Comment: Published versio

Dissipationless counterflow currents above T_c in bilayer superconductors

We report the existence of dissipationless currents in bilayer superconductors above the critical temperature $T_c$, assuming that the superconducting phase transition is dominated by phase fluctuations. Using a semiclassical $U(1)$ lattice gauge theory, we show that thermal fluctuations cause a transition from the superconducting state at low temperature to a resistive state above $T_c$, accompanied by the proliferation of unbound vortices. Remarkably, while the proliferation of vortex excitations causes dissipation of homogeneous in-plane currents, we find that counterflow currents, flowing in opposite direction within a bilayer, remain dissipationless. The presence of a dissipationless current channel above $T_c$ is attributed to the inhibition of vortex motion by local superconducting coherence within a single bilayer, in the presence of counterflow currents. Our theory presents a possible scenario for the pseudogap phase in bilayer cuprates.Comment: Main text : 4 pages, 4 figures. Supplement: 8 pages, 9 figure

Self-similar dynamics of order parameter fluctuations in pump-probe experiments

Upon excitation by a laser pulse, broken-symmetry phases of a wide variety of solids demonstrate similar order parameter dynamics characterized by a dramatic slowing down of relaxation for stronger pump fluences. Motivated by this recurrent phenomenology, we develop a simple non-perturbative effective model of dynamics of collective bosonic excitations in pump-probe experiments. We find that as the system recovers after photoexcitation, it shows universal prethermalized dynamics manifesting a power-law, as opposed to exponential, relaxation, explaining the slowing down of the recovery process. For strong quenches, long-wavelength over-populated transverse modes dominate the long-time dynamics; their distribution function exhibits universal scaling in time and space, whose universal exponents can be computed analytically. Our model offers a unifying description of order parameter fluctuations in a regime far from equilibrium, and our predictions can be tested with available time-resolved techniques

Principles of 2D terahertz spectroscopy of collective excitations: the case of Josephson plasmons in layered superconductors

Two-dimensional terahertz spectroscopy (2DTS), a terahertz analogue of nuclear magnetic resonance, is a new technique poised to address many open questions in complex condensed matter systems. The conventional theoretical framework used ubiquitously for interpreting multidimensional spectra of discrete quantum level systems is, however, insufficient for the continua of collective excitations in strongly correlated materials. Here, we develop a theory for 2DTS of a model collective excitation, the Josephson plasma resonance in layered superconductors. Starting from a mean-field approach at temperatures well below the superconducting phase transition, we obtain expressions for the multidimensional nonlinear responses that are amenable to intuition derived from the conventional single-mode scenario. We then consider temperatures near the superconducting critical temperature $T_c$, where dynamics beyond mean-field become important and conventional intuition fails. As fluctuations proliferate near $T_c$, the dominant contribution to nonlinear response comes from an optical parametric drive of counter-propagating Josephson plasmons, which gives rise to 2D spectra that are qualitatively different from the mean-field predictions. As such, and in contrast to one-dimensional spectroscopy techniques, such as third harmonic generation, 2DTS can be used to directly probe thermally excited finite-momentum plasmons and their interactions. Our theory provides a clear interpretation of recent 2DTS measurements on cuprates, and we discuss implications beyond the present context of Josephson plasmons

Generalized Fresnel-Floquet equations for driven quantum materials

Optical drives at terahertz and midinfrared frequencies in quantum materials are increasingly used to reveal the nonlinear dynamics of collective modes in correlated many-body systems and their interplay with electromagnetic waves. Recent experiments demonstrated several surprising optical properties of transient states induced by driving, including the appearance of photo-induced edges in the reflectivity in cuprate superconductors (SCs), observed both below and above the equilibrium transition temperature. Furthermore, in other driven materials, reflection coefficients larger than unity have been observed. In this paper we demonstrate that unusual optical properties of photoexcited systems can be understood from the perspective of a Floquet system, a system with periodically modulated parameters originating from pump-induced oscillations of a collective mode. These oscillations lead to an effective Floquet system with periodically modulated parameters. We present a general phenomenological model of reflectivity from Floquet materials, which takes into account parametric generation of excitation pairs. We find a universal phase diagram of drive-induced features in reflectivity which evidence a competition between driving and dissipation. To illustrate our general analysis, we apply our formalism to two concrete examples motivated by recent experiments: A single plasmon band, which describes Josephson plasmons (JPs) in layered SCs, and a phonon-polariton system, which describes upper and lower polaritons in materials such as insulating SiC. Finally, we demonstrate that our model can be used to provide an accurate fit to results of phonon-pump–terahertz-probe experiments in the high-temperature SC YBa2Cu3O6.5. Our model explains the appearance of a pump-induced edge, which is higher in energy than the equilibrium JP edge, even if the interlayer Josephson coupling is suppressed by the pump pulse

Periodic dynamics in superconductors induced by an impulsive optical quench

A number of experiments have evidenced signatures of enhanced superconducting correlations after photoexcitation. Initially, these experiments were interpreted as resulting from quasi-static changes in the Hamiltonian parameters, for example, due to lattice deformations or melting of competing phases. Yet, several recent observations indicate that these conjectures are either incorrect or do not capture all the observed phenomena, which include reflectivity exceeding unity, large shifts of Josephson plasmon edges, and appearance of new peaks in terahertz reflectivity. These observations can be explained from the perspective of a Floquet theory involving a periodic drive of system parameters, but the origin of the underlying oscillations remains unclear. In this paper, we demonstrate that following incoherent photoexcitation, long-lived oscillations are generally expected in superconductors with low-energy Josephson plasmons, such as in cuprates or fullerene superconductor K3C60. These oscillations arise from the parametric generation of plasmon pairs due to pump-induced perturbation of the superconducting order parameter. We show that this bi-plasmon response can persist even above the transition temperature as long as strong superconducting fluctuations are present. Our analysis offers a robust framework to understand light-induced superconducting behavior, and the predicted bi-plasmon oscillations can be directly detected using available experimental techniques

Mechanisms for Long-Lived, Photo-Induced Superconductivity

Advances in the control of intense infrared light have led to the striking discovery of metastable superconductivity in $\mathrm{K}_3\mathrm{C}_{60}$ at 100K, lasting more than 10 nanoseconds. Inspired by these experiments, we discuss possible mechanisms for long-lived, photo-induced superconductivity above $T_{c}$. We analyze a minimal model of optically-driven Raman phonons coupled to inter-band electronic transitions. Using this model, we develop a possible microscopic mechanism for photo-controlling the pairing interaction by displacively shifting the Raman mode. Leveraging this mechanism, we explore two pictures of long-lived, light-induced superconductivity far above $T_c$. We first investigate long-lived, photo-induced superconductivity arising from the metastable trapping of a displaced phonon coordinate. We then propose an alternate route to long-lived superconductivity. Within this paradigm, the slow equilibration of quasi-particles enables a long-lived, non-thermal superconducting gap. We conclude by discussing implications of both scenarios to experiments that can be used to discriminate between them. Our work provides falsifiable, mechanistic explanations for the nanosecond scale photo-induced superconductivity found in $\mathrm{K}_3\mathrm{C}_{60}$, while also offering a theoretical basis for exploring long-lived, non-equilibrium superconductivity in other quantum materials.Comment: 7 pages Main Text, 9 pages Supplementary Material, 4 figure

Probing Inhomogeneous Cuprate Superconductivity by Terahertz Josephson Echo Spectroscopy

Inhomogeneities play a crucial role in determining the properties of quantum materials. Yet methods that can measure these inhomogeneities are few, and apply to only a fraction of the relevant microscopic phenomena. For example, the electronic properties of cuprate materials are known to be inhomogeneous over nanometer length scales, although questions remain about how such disorder influences supercurrents and their dynamics. Here, two-dimensional terahertz spectroscopy is used to study interlayer superconducting tunneling in near-optimally-doped La1.83Sr0.17CuO4. We isolate a 2 THz Josephson echo signal with which we disentangle intrinsic lifetime broadening from extrinsic inhomogeneous broadening. We find that the Josephson plasmons are only weakly inhomogeneously broadened, with an inhomogeneous linewidth that is three times smaller than their intrinsic lifetime broadening. This extrinsic broadening remains constant up to 0.7Tc, above which it is overcome by the thermally-increased lifetime broadening. Crucially, the effects of disorder on the Josephson plasma resonance are nearly two orders of magnitude smaller than the in-plane variations in the superconducting gap in this compound, which have been previously documented using Scanning Tunnelling Microscopy (STM) measurements. Hence, even in the presence of significant disorder in the superfluid density, the finite frequency interlayer charge fluctuations exhibit dramatically reduced inhomogeneous broadening. We present a model that relates disorder in the superfluid density to the observed lifetimes