arXiv subjects

Christoph Bruder

Publications and source records attributed to Christoph Bruder.

At least 55 records · Page 3Linked to original sources

arXiv2016

Genuine quantum signatures in synchronization of anharmonic self-oscillators

We study the synchronization of a van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system. Strong driving close to these resonances leads to nonclassical steady-state Wigner distributions. Experimental realizations of these genuine quantum signatures can be implemented with current technology.

quant-ph↗

arXiv2016

Thermoelectricity in a junction between interacting cold atomic Fermi gases

A gas of interacting ultracold fermions can be tuned into a strongly interacting regime using a Feshbach resonance. Here we theoretically study quasiparticle transport in a system of two reservoirs of interacting ultracold fermions on the BCS side of the BCS-BEC crossover coupled weakly via a tunnel junction. Using the generalized BCS theory we calculate the time evolution of the system that is assumed to be initially prepared in a non-equilibrium state characterized by a particle number imbalance or a temperature imbalance. A number of characteristic features like sharp peaks in quasiparticle currents, or transitions between the normal and superconducting states are found. We discuss signatures of the Seebeck and the Peltier effect and the resulting temperature difference of the two reservoirs as a function of the interaction parameter $(k_Fa)^{-1}$. The Peltier effect may lead to an additional cooling mechanism for ultracold fermionic atoms.

cond-mat.quant-gas↗

arXiv2016

Optomechanical Self-Oscillations in an Anharmonic Potential: Engineering a Nonclassical Steady State

We study self-oscillations of an optomechanical system, where coherent mechanical oscillations are induced by a driven optical or microwave cavity, for the case of an anharmonic mechanical oscillator potential. A semiclassical analytical model is developed to characterize the limit cycle for large mechanical amplitudes corresponding to a weak nonlinearity. As a result, we predict conditions to achieve subpoissonian phonon statistics in the steady state, indicating classically forbidden behavior. We compare with numerical simulations and find very good agreement. Our model is quite general and can be applied to other physical systems such as trapped ions or superconducting circuits.

quant-ph↗

arXiv2016

Dynamics of Hubbard Hamiltonians with the multiconfigurational time-dependent Hartree method for indistinguishable particles

We apply the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X) to systems of bosons or fermions in lattices described by Hubbard type Hamiltonians with long-range or short-range interparticle interactions. The wavefunction is expanded in a variationally optimized time-dependent many-body basis generated by a set of effective creation operators that are related to the original particle creation operators by a time-dependent unitary transform. We use the time-dependent variational principle for the coefficients of this transform as well as the expansion coefficients of the wavefunction in the time-dependent many-body basis as variational parameters to derive equations of motion. The convergence of MCTDH-X is shown by comparing its results to the exact diagonalization of one-, two-, and three-dimensional lattices filled with bosons with contact interactions. We use MCTDH-X to study the buildup of correlations in the long-time splitting dynamics of a Bose-Einstein condensate loaded into a large two-dimensional lattice subject to a barrier that is ramped up in the center. We find that the system is split into two parts with emergent time-dependent correlations that depend on the ramping time -- for most barrier-raising-times the system becomes two-fold fragmented, but for some of the very fast ramps, the system shows revivals of coherence.

cond-mat.quant-gas↗

arXiv2016

The topological Anderson insulator phase in the Kane-Mele model

It has been proposed that adding disorder to a topologically trivial mercury telluride/cadmium telluride (HgTe/CdTe) quantum well can induce a transition to a topologically nontrivial state. The resulting state was termed topological Anderson insulator and was found in computer simulations of the Bernevig-Hughes-Zhang model. Here, we show that the topological Anderson insulator is a more universal phenomenon and also appears in the Kane-Mele model of topological insulators on a honeycomb lattice. We numerically investigate the interplay of the relevant parameters, and establish the parameter range in which the topological Anderson insulator exists. A staggered sublattice potential turns out to be a necessary condition for the transition to the topological Anderson insulator. For weak enough disorder, a calculation based on the lowest-order Born approximation reproduces quantitatively the numerical data. Our results thus considerably increase the number of candidate materials for the topological Anderson insulator phase.

cond-mat.mes-hall↗

arXiv2015

Full counting statistics of Majorana interferometers

We study the full counting statistics of interferometers for chiral Majorana fermions with two incoming and two outgoing Dirac fermion channels. In the absence of interactions, the FCS can be obtained from the $4\times4$ scattering matrix $S$ that relates the outgoing Dirac fermions to the incoming Dirac fermions. After presenting explicit expressions for the higher-order current correlations for a modified Hanbury Brown-Twiss interferometer, we note that the cumulant-generating function can be interpreted such that unit-charge transfer processes correspond to two independent half-charge transfer processes, or alternatively, to two independent electron-hole conversion processes. By a combination of analytical and numerical approaches, we verify that this factorization property holds for a general $SO(4)$ scattering matrix, i.e. for a general interferometer geometry.

cond-mat.mes-hall↗

arXiv2014

Detection of weak forces based on noise-activated switching in bistable optomechanical systems

We propose to use cavity optomechanical systems in the regime of optical bistability for the detection of weak harmonic forces. Due to the optomechanical coupling an external force on the mechanical oscillator modulates the resonance frequency of the cavity and consequently the switching rates between the two bistable branches. A large difference in the cavity output fields then leads to a strongly amplified homodyne signal. We determine the switching rates as a function of the cavity detuning from extensive numerical simulations of the stochastic master equation as appropriate for continuous homodyne detection. We develop a two-state rate equation model that quantitatively describes the slow switching dynamics. This model is solved analytically in the presence of a weak harmonic force to obtain approximate expressions for the power gain and signal-to-noise ratio that we then compare to force detection with an optomechanical system in the linear regime.

quant-ph↗

arXiv2014

Quantum synchronization of two Van der Pol oscillators

We study synchronization of two dissipatively coupled Van der Pol oscillators in the quantum regime. Due to quantum noise strict frequency locking is absent and is replaced by a crossover from weak to strong frequency entrainment. We discuss the differences to the behavior of one quantum Van der Pol oscillator subject to an external drive. Moreover, we describe a possible experimental realization of two coupled quantum van der Pol oscillators in an optomechanical setting.

cond-mat.mes-hall↗

arXiv2014

Josephson effect in normal and ferromagnetic topological insulator planar, step and edge junctions

We investigate Josephson junctions on the surface of a three-dimensional topological insulator in planar, step, and edge geometries. The elliptical nature of the Dirac cone representing the side surface states of the topological insulator results in a scaling factor in the Josephson current in a step junction as compared to the planar junction. In edge junctions, the contribution of the Andreev bound states to the Josephson current vanishes due to spin-momentum locking of the surface states. Furthermore, we consider a junction with a ferromagnetic insulator between the superconducting regions. In these ferromagnetic junctions, we find an anomalous finite Josephson current at zero phase difference if the magnetization is pointing along the junction (and perpendicular to the Josephson current). An out-of-plane magnetization with respect to the central region of the junction opens up an exchange gap and leads to a non-monotonic behavior of the critical Josephson current for sufficiently large magnetization as the chemical potential increases.

cond-mat.mes-hall↗

arXiv2014

Quantum synchronization of a driven self-sustained oscillator

Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical self-sustained oscillator coupled to an external harmonic drive. Using the power spectrum we analyze synchronization in terms of frequency entrainment and frequency locking in close analogy to the classical case. We show that there is a step-like crossover to a synchronized state as a function of the driving strength. In contrast to the classical case, there is a finite threshold value in driving. Quantum noise reduces the synchronized region and leads to a deviation from strict frequency locking.

cond-mat.mes-hall↗

arXiv2013

Equivalence between an optomechanical system and a Kerr medium

We study the optical bistability of an optomechanical system in which the position of a mechanical oscillator modulates the cavity frequency. The steady-state mean-field equation of the optical mode is identical to the one for a Kerr medium, and thus we expect it to have the same characteristic behavior with a lower, a middle, and an upper branch. However, the presence of position fluctuations of the mechanical resonator leads to a new feature: the upper branch will become unstable at sufficiently strong driving in certain parameter regimes. We identify the appropriate parameter regime for the upper branch to be stable, and we confirm, by numerical investigation of the quantum steady state, that the mechanical mode indeed acts as a Kerr nonlinearity for the optical mode in the low-temperature limit. This equivalence of the optomechanical system and the Kerr medium will be important for future applications of cavity optomechanics in quantum nonlinear optics and quantum information science.

quant-ph↗

arXiv2013

Nonsymmetrized Correlations in Quantum Noninvasive Measurements

A long-standing problem in quantum mesoscopic physics is which operator order corresponds to noise expressions like , where I(ω) is the measured current at frequency ω. Symmetrized order describes a classical measurement while nonsymmetrized order corresponds to a quantum detector, e.g., one sensitive to either emission or absorption of photons. We show that both order schemes can be embedded in quantum weak-measurement theory taking into account measurements with memory, characterized by a memory function which is independent of a particular experimental detection scheme. We discuss the resulting quasiprobabilities for different detector temperatures and how their negativity can be tested on the level of second-order correlation functions already. Experimentally, this negativity can be related to the squeezing of the many-body state of the transported electrons in an ac-driven tunnel junction.

quant-ph↗

arXiv2013

Strong-coupling effects in dissipatively coupled optomechanical systems

In this paper we study cavity optomechanical systems in which the position of a mechanical oscillator modulates both the resonance frequency (dispersive coupling) and the linewidth (dissipative coupling) of a cavity mode. Using a quantum noise approach we calculate the optical damping and the optically-induced frequency shift. We find that dissipatively coupled systems feature two parameter regions providing amplification and two parameter regions providing cooling. To investigate the strong-coupling regime, we solve the linearized equations of motion exactly and calculate the mechanical and optical spectra. In addition to signatures of normal-mode splitting that are similar to the case of purely dispersive coupling, the spectra contain a striking feature that we trace back to the Fano line shape of the force spectrum. Finally, we show that purely dissipative coupling can lead to optomechanically-induced transparency which will provide an experimentally convenient way to observe normal-mode splitting.

quant-ph↗

arXiv2013

Strategy for implementing stabilizer-based codes on solid-state qubits

We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the "standard" five-qubit and CSS codes, on solid-state qubits with Ising or XY-type interactions. Using pulse sequences, we show how to induce the effective dynamics of the stabilizer Hamiltonian, the sum of an appropriate set of stabilizer operators for a given code. Within this approach, the encoded states (ground states of the stabilizer Hamiltonian) can be prepared without measurements and preserved against both the time evolution governed by the original qubit Hamiltonian, and energy-nonconserving errors caused by the environment.

quant-ph↗

arXiv2013

Microwave-controlled coupling of Majorana bound states

We propose microwave-controlled rotations for qubits realized as Majorana bound states. To this end we study an inhomogeneous Kitaev chain in a microwave cavity. The chain consists of two topologically nontrivial regions separated by a topologically trivial, gapped region. The Majorana bound states at the interfaces between the left (right) regions and the central region are coupled, and their energies are split by virtual cotunneling processes. The amplitude for these cotunneling processes decreases exponentially in the number of sites of the gapped region, and the decay length diverges as the gap of the topologically trivial region closes. We demonstrate that microwave radiation can exponentially enhance the coupling between the Majorana bound states, both for classical and quantized electric fields. By solving the appropriate Liouville equation numerically we show that microwaves can drive Rabi oscillations in the Majorana sector. Our model emerges as an effective description for a topological semiconductor nanowire in a microwave cavity. Thus, our proposal provides an experimentally feasible way to obtain full single-qubit control necessary for universal quantum computation with Majorana qubits.

cond-mat.mes-hall↗

arXiv2013

Majorana qubit rotations in microwave cavities

Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states. These oscillations can be used to implement an additional single-qubit gate. Supplemented with one braiding operation, this gate allows to perform arbitrary single-qubit operations.

cond-mat.mes-hall↗

arXiv2012

Preserving universal resources for one-way quantum computing

The common spin Hamiltonians such as the Ising, XY, or Heisenberg model do not have ground states that are the graph states needed in measurement-based quantum computation. Various highly-entangled many-body states have been suggested as a universal resource for this type of computation, however, it is not easy to preserve these states in solid-state systems due to their short coherence times. Here we propose a scheme for generating a Hamiltonian that has a cluster state as ground state. Our approach employs a series of pulse sequences inspired by established NMR techniques and holds promise for applications in many areas of quantum information processing.

cond-mat.str-el↗

arXiv2012

Mean-Field Analysis of Spinor Bosons in Optical Superlattices

We study the ground-state phase diagram of spinless and spin-1 bosons in optical superlattices using a Bose-Hubbard Hamiltonian that includes spin-dependent interactions. We decouple the unit cells of the superlattice via a mean-field approach and take into account the dynamics within the unit cell exactly. The system supports Mott-insulating as well as superfluid phases. The transitions between these phases are second-order for spinless bosons and second- or first-order for spin-1 bosons. Anti-ferromagnetic interactions energetically penalize high-spin configurations and elongate all Mott lobes, especially the ones corresponding to an even atom number on each lattice site. We find that the quadratic Zeeman effect lifts the degeneracy between different polar superfluid phases leading to additional metastable phases and first-order phase transitions. Finally, we show that an energy offset between the two sites of the unit cell induces a staircase of single-atom tunneling resonances which surprisingly survives well into the superfluid regime.

cond-mat.quant-gas↗