Luminescence and Squeezing of a Superconducting Light Emitting Diode

We investigate a semiconductor $p$-$n$ junction in contact with superconducting leads that is operated under forward bias as a light-emitting diode. The presence of superconductivity results in a significant increase of the electroluminescence in a certain frequency window. We demonstrate that the tunneling of Cooper pairs induces an additional luminescence peak on resonance. There is a transfer of superconducting to photonic coherence which results in the emission of entangled photon pairs and squeezing of the fluctuations in the quadrature amplitudes of the emitted light. The squeezing angle can be electrically manipulated by changing the relative phase of the order parameters in the superconductors. We finally derive the conditions for lasing in the system and show that the laser threshold is reduced due to superconductivity. This shows how macroscopic coherence of a superconductor can be used to control the properties of light.Comment: 26 pages, 14 figures. Published versio

Dimensional crossover and cold-atom realization of topological Mott insulators

We propose a cold-atom setup which allows for a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers. We further show that additional Hubbard onsite interactions can give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of a quantum state of matter which merely exists because of the interplay of the non-trivial topology of the band structure and strong interactions. While the theoretical understanding of this phase has remained elusive, our proposal shall help to shed some light on this exotic state of matter by paving the way for a controlled experimental investigation in optical lattices.Comment: 4+ pages, 3 figures; includes Supplemental Material (3 pages, 1 figure

Non-perturbative stochastic method for driven spin-boson model

We introduce and apply a numerically exact method for investigating the real-time dissipative dynamics of quantum impurities embedded in a macroscopic environment beyond the weak-coupling limit. We focus on the spin-boson Hamiltonian that describes a two-level system interacting with a bosonic bath of harmonic oscillators. This model is archetypal for investigating dissipation in quantum systems and tunable experimental realizations exist in mesoscopic and cold-atom systems. It finds abundant applications in physics ranging from the study of decoherence in quantum computing and quantum optics to extended dynamical mean-field theory. Starting from the real-time Feynman-Vernon path integral, we derive an exact stochastic Schr\"odinger equation that allows to compute the full spin density matrix and spin-spin correlation functions beyond weak coupling. We greatly extend our earlier work (P. P. Orth, A. Imambekov, and K. Le Hur, Phys. Rev. A {\bf 82}, 032118 (2010)) by fleshing out the core concepts of the method and by presenting a number of interesting applications. Methodologically, we present an analogy between the dissipative dynamics of a quantum spin and that of a classical spin in a random magnetic field. This analogy is used to recover the well-known non-interacting-blip-approximation in the weak-coupling limit. We explain in detail how to compute spin-spin autocorrelation functions. As interesting applications of our method, we explore the non-Markovian effects of the initial spin-bath preparation on the dynamics of the coherence $\sigma^x(t)$ and of $\sigma^z(t)$ under a Landau-Zener sweep of the bias field. We also compute to a high precision the asymptotic long-time dynamics of $\sigma^z(t)$ without bias and demonstrate the wide applicability of our approach by calculating the spin dynamics at non-zero bias and different temperatures.Comment: 25 pages, 10 figure

Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment

In an extensive computational experiment, we test Polyakov's conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multi-spin $\text{U(1)}$ order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling, we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type and at lower temperatures, we find long-range $\mathbb{Z}_6$ order.Comment: 4+ pages, 4 figures; includes Supplemental Material (5 pages, 1 figure

Universal post-quench coarsening and quantum aging at a quantum critical point

The non-equilibrium dynamics of a system that is located in the vicinity of a quantum critical point is affected by the critical slowing down of order-parameter correlations with the potential for novel out-of-equilibrium universality. After a quantum quench, i.e. a sudden change of a parameter in the Hamiltonian such a system is expected to almost instantly fall out of equilibrium and undergo aging dynamics, i.e. dynamics that depends on the time passed since the quench. Investigating the quantum dynamics of a $N$-component $\varphi^{4}$-model coupled to an external bath, we determine this universal aging and demonstrate that the system undergoes a coarsening, governed by a critical exponent that is unrelated to the equilibrium exponents of the system. We analyze this behavior in the large-$N$ limit, which is complementary to our earlier renormalization group analysis, allowing in particular the direct investigation of the order-parameter dynamics in the symmetry broken phase and at the upper critical dimension. By connecting the long time limit of fluctuations and response, we introduce a distribution function that shows that the system remains non-thermal and exhibits quantum coherence even on long timescales.Comment: 25 pages, 6 figure

Manipulation of a two-photon pump in superconductor - semiconductor heterostructures

We investigate the photon statistics, entanglement and squeezing of a pn-junction sandwiched between two superconducting leads, and show that such an electrically-driven photon pump generates correlated and entangled pairs of photons. In particular, we demonstrate that the squeezing of the fluctuations in the quadrature amplitudes of the emitted light can be manipulated by changing the relative phase of the order parameters of the superconductors. This reveals how macroscopic coherence of the superconducting state can be used to tailor the properties of a two-photon state.Comment: 4+ pages, 3 figures; includes Supplemental Material (9 pages, 1 figure). Published versio

Universality in dissipative Landau-Zener transitions

We introduce a random variable approach to investigate the dynamics of a dissipative two-state system. Based on an exact functional integral description, our method reformulates the problem as that of the time evolution of a quantum state vector subject to a Hamiltonian containing random noise fields. This numerically exact, non-perturbative formalism is particularly well suited in the context of time-dependent Hamiltonians, both at zero and finite temperature. As an important example, we consider the renowned Landau-Zener problem in the presence of an Ohmic environment with a large cutoff frequency at finite temperature. We investigate the 'scaling' limit of the problem at intermediate times, where the decay of the upper spin state population is universal. Such a dissipative situation may be implemented using a cold-atom bosonic setup.Comment: 6 pages, 2 figs; added finite temperature result