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Michael R. Geller

Publications and source records attributed to Michael R. Geller.

At least 55 records · Page 3Linked to original sources

Hot-electron Effect in A Cylindrical Nanoshell

A general expression for calculating the thermal power transferring from 3-dimensional electron to any D-dimensional phonon subsystem is derived in this paper. Electron-phonon coupling in a free suspended cylindrical nanoshell is studied, in which acoustic phonons are confined to quasi-one dimension but electrons behave three-dimensionally. The temperature dependence of the thermal power is obtained analytically, and the low-temperature crossover from the $T^{3}$ to $T^{3}/(1-ν^2)+9γT^4/[T^*(1-ν^2)^{3/2}]$ dependence is also observed. The corresponding quantities are estimated for the material parameters from a metallic nanotube.

cond-mat.mes-hall↗

Quantum computation with prethreshold superconducting qubits: Single-excitation subspace approach

We describe an alternative approach to quantum computation that is ideally suited for today's sub-threshold-fidelity qubits, and which can be applied to a family of hardware models that includes superconducting qubits with tunable coupling. In this approach, the computation on an n-qubit processor is carried out in the n-dimensional single-excitation subspace (SES) of the full 2^n-dimensional Hilbert space. Because any real Hamiltonian can be directly generated in the SES [E. J. Pritchett et al., arXiv:1008.0701], high-dimensional unitary operations can be carried out in a single step, bypassing the need to decompose into single- and two-qubit gates. Although technically nonscalable and unsuitable for applications (including Shor's) requiring enormous Hilbert spaces, this approach would make practical a first-generation quantum computer capable of achieving significant quantum speedup.

quant-ph↗

Analysis of a tuneable coupler for superconducting phase qubits

This paper presents a theoretical analysis of the recently realized tuneable coupler for superconducting phase qubits (R. C. Bialczak et al., Ref.\ \protect\onlinecite{Bialczak}). The coupling can be turned off by compensating a negative mutual inductance with a tuneable Josephson inductance. The main coupling in this system is of the $XX$ type and can be zeroed exactly, while there is also a small undesired contribution of the $ZZ$ type. We calculate both couplings as functions of the tuning parameter (bias current) and focus on the residual coupling in the OFF regime. In particular, we show that for typical experimental parameters the coupling OFF/ON ratio is few times $10^{-3}$, and it may be zeroed by proper choice of parameters. The remaining errors due to physical presence of the coupler are on the order of $10^{-6}$.

cond-mat.mes-hall↗

Quantum Simulation of Molecular Collisions with Superconducting Qubits

We introduce a protocol for the fast simulation of $n$-dimensional quantum systems on $n$-qubit quantum computers with tunable couplings. A mapping is given between the control parameters of the quantum computer and the matrix elements of $H_{\rm s}(t)$, an arbitrary, real, time-dependent $n\times n$ dimensional Hamiltonian that is simulated in the $n$-dimensional `single excitation' subspace of the quantum computer. A time-dependent energy/time rescaling minimizes the simulation time on hardware having a fixed coherence time. We demonstrate how three tunably coupled phase qubits simulate a three-channel molecular collision using this protocol, then study the simulation's fidelity as a function of total simulation time.

quant-ph↗

Controlled-NOT gate with weakly coupled qubits: Dependence of fidelity on the form of interaction

An approach to the construction of the CNOT quantum logic gate for a 4-dimensional coupled-qubit model with weak but otherwise arbitrary coupling has been given recently [M. R. Geller et al., Phys. Rev. A, 012320 (2010)]. How does the resulting fidelity depend on the form of qubit-qubit coupling? In this paper we calculate intrinsic fidelity curves (fidelity in the absence of decoherence versus total gate time) for a variety of qubit-qubit interactions, including the commonly occurring isotropic Heisenberg and XY models, as well as randomly generated ones. For interactions not too close to that of the Ising model, we find that the fidelity curves do not significantly depend on the form of the interaction, and we calculate the resulting interaction-averaged fidelity curve for the non-Ising-like cases and a criterion for determining its applicability.

quant-ph↗

Quantum logic with weakly coupled qubits

There are well-known protocols for performing CNOT quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or qubits and resonators coupled by more complicated and less symmetric interactions. Here we consider a widely applicable model of weakly but otherwise arbitrarily coupled two-level systems, and use quantum gate design techniques to derive a simple and intuitive CNOT construction. Useful variations and extensions of the solution are given for common special cases.

quant-ph↗

Tunneling into a Fractional Quantum Hall System and the Infrared Catastrophe

We calculate the tunneling density of states of a two-dimensional interacting electron gas in a quantizing magnetic field. We show that the observed pseudogap in the density of states can be understood as the result of an infrared catastrophe in a noninteracting electron model. This catastrophe stems from the response of an electronic system to the potential produced by the abruptly added charge during a tunneling event. Our formalism can be applied at any filling factor without the use of Chern-Simons or composite fermion theory.

cond-mat.mes-hall↗

Quantum computing with superconductors I: Architectures

Josephson junctions have demonstrated enormous potential as qubits for scalable quantum computing architectures. Here we discuss the current approaches for making multi-qubit circuits and performing quantum information processing with them.

quant-ph↗

Aharonov-Bohm effect in the non-Abelian quantum Hall fluid

The nu=5/2 fractional quantum Hall effect state has attracted great interest recently, both as an arena to explore the physics of non-Abelian quasiparticle excitations, and as a possible architecture for topological quantum information processing. Here we use the conformal field theoretic description of the Moore-Read state to provide clear tunneling signatures of this state in an Aharonov-Bohm geometry. While not probing statistics directly, the measurements proposed here would provide a first, experimentally tractable step towards a full characterization of the 5/2 state.

cond-mat.mes-hall↗

Friction in nanoelectromechanical systems: Clamping loss in the GHz regime

The performance of a wide variety of ultra-sensitive devices employing nanoelectromechanical resonators is determined by their mechanical quality factor, yet energy dissipation in these systems remains poorly understood. Here we develop a comprehensive theory of friction in high frequency resonators caused by the radiation of elastic energy into the support substrate, referred to as clamping loss. The elastic radiation rate is found to be a strong increasing function of resonator frequency, and we argue that this mechanism will play an important role in future microwave-frequency devices.

cond-mat.mtrl-sci↗

Infrared catastrophe and tunneling into strongly correlated electron systems: Exact solution of the x-ray edge limit for the 1D electron gas and 2D Hall fluid

In previous work we have proposed that the non-Fermi-liquid spectral properties in a variety of low-dimensional and strongly correlated electron systems are caused by the infrared catastrophe, and we used an exact functional integral representation for the interacting Green's function to map the tunneling problem onto the x-ray edge problem, plus corrections. The corrections are caused by the recoil of the tunneling particle, and, in systems where the method is applicable, are not expected to change the qualitative form of the tunneling density of states (DOS). Qualitatively correct results were obtained for the DOS of the 1D electron gas and 2D Hall fluid when the corrections to the x-ray edge limit were neglected and when the corresponding Nozieres-De Dominicis integral equations were solved by resummation of a divergent perturbation series. Here we reexamine the x-ray edge limit for these two models by solving these integral equations exactly, finding the expected modifications of the DOS exponent in the 1D case but finding no changes in the DOS of the 2D Hall fluid with short-range interaction. We also provide, for the first time, an exact solution of the Nozieres-De Dominicis equation for the 2D electron gas in the lowest Landau level.

cond-mat.str-el↗

Infrared catastrophe and tunneling into strongly correlated electron systems: Beyond the x-ray edge limit

We develop a nonperturbative method to calculate the electron propagator in low-dimensional and strongly correlated electron systems. The method builds on our earlier work using a Hubbard-Stratonovich transformation to map the tunneling problem to the x-ray edge problem, which accounts for the infrared catastrophe caused by the sudden introduction of a new electron into a conductor during a tunneling event. Here we use a cumulant expansion to include fluctuations about this x-ray edge limit. We find that the dominant effect of electron-electron interaction at low energies is to correct the noninteracting Green's function by a factor exp(-S), where S can be interpreted as the Euclidean action for a density field describing the time-dependent charge distribution of the newly added electron. Initially localized, this charge distribution spreads in time as the electron is accommodated by the host conductor, and during this relaxation process action is accumulated according to classical electrostatics with a screened interaction. The theory applies to lattice or continuum models of any dimensionality, with or without translational invariance. In one dimension the method correctly predicts a power-law density of states (DOS) for electrons with short-range interaction and no disorder, and when applied to the solvable Tomonaga-Luttinger model, the exact DOS is obtained.

cond-mat.str-el↗

Infrared catastrophe and tunneling into strongly correlated electron systems: Perturbative x-ray edge limit

The tunneling density of states exhibits anomalies (cusps, algebraic suppressions, and pseudogaps) at the Fermi energy in a wide variety of low-dimensional and strongly correlated electron systems. We argue that in many cases these spectral anomalies are caused by an infrared catastrophe in the screening response to the sudden introduction of a new electron into the system during a tunneling event. A nonperturbative functional-integral method is introduced to account for this effect, making use of methods developed for the x-ray edge singularity problem. The formalism is applicable to lattice or continuum models of any dimensionality, with or without translational invariance. An approximate version of the technique is applied to the 1D electron gas and the 2D Hall fluid, yielding qualitatively correct results.

cond-mat.str-el↗

Nanomechanical Quantum Memory for Superconducting Qubits

Many protocols for quantum computation require a quantum memory element to store qubits. We discuss the accuracy with which quantum states prepared in a Josephson junction qubit can be stored in a nanoelectromechanical resonator and then transfered back to the junction. We find that the fidelity of the memory operation depends on both the junction-resonator coupling strength and the location of the state on the Bloch sphere. Although we specifically focus on a large-area, current-biased Josesphson junction phase qubit coupled to the dilatational mode of a piezoelectric nanoelectromechanical disk resonator, many our results will apply to other qubit-oscillator models.

quant-ph↗

Superconducting Qubits Coupled to Nanoelectromechanical Resonators: An Architecture for Solid-State Quantum Information Processing

We describe the design for a scalable, solid-state quantum-information-processing architecture based on the integration of GHz-frequency nanomechanical resonators with Josephson tunnel junctions, which has the potential for demonstrating a variety of single- and multi-qubit operations critical to quantum computation. The computational qubits are eigenstates of large-area, current-biased Josephson junctions, manipulated and measured using strobed external circuitry. Two or more of these phase qubits are capacitively coupled to a high-quality-factor piezoelectric nanoelectromechanical disk resonator, which forms the backbone of our architecture, and which enables coherent coupling of the qubits. The integrated system is analogous to one or more few-level atoms (the Josephson junction qubits) in an electromagnetic cavity (the nanomechanical resonator). However, unlike existing approaches using atoms in electromagnetic cavities, here we can individually tune the level spacing of the ``atoms'' and control their ``electromagnetic'' interaction strength. We show theoretically that quantum states prepared in a Josephson junction can be passed to the nanomechanical resonator and stored there, and then can be passed back to the original junction or transferred to another with high fidelity. The resonator can also be used to produce maximally entangled Bell states between a pair of Josephson junctions. Many such junction-resonator complexes can assembled in a hub-and-spoke layout, resulting in a large-scale quantum circuit. Our proposed architecture combines desirable features of both solid-state and cavity quantum electrodynamics approaches, and could make quantum information processing possible in a scalable, solid-state environment.

quant-ph↗

Mesoscopic Phonon Transmission through a Nanowire-Bulk Contact

We calculate the frequency-dependent mesoscopic acoustic phonon transmission probability through the abrupt junction between a semi-infinite, one-dimensional cylindrical quantum wire and a three-dimensional bulk insulator, using a perturbative technique that is valid at low frequency. The system is described using elasticity theory, and traction-free boundary conditions are applied to all free surfaces. In the low-frequency limit the transmission probability vanishes as the frequency squared, the transport being dominated by the longitudinal channel, which produces a monopole source of elastic radiation at the surface of the bulk solid. The thermal conductance between an equilibrated wire nonadiabatically coupled to a bulk insulator should therefore vanish with temperature at temperature cubed.

cond-mat.mes-hall↗

Superconducting Phase Qubit Coupled to a Nanomechanical Resonator: Beyond the Rotating-Wave Approximation

We consider a simple model of a Josephson junction phase qubit coupled to a solid-state nanoelectromechanical resonator. This and many related qubit-resonator models are analogous to an atom in an electromagnetic cavity. When the systems are weakly coupled and nearly resonant, the dynamics is accurately described by the rotating-wave approximation (RWA) or the Jaynes-Cummings model of quantum optics. However, the desire to develop faster quantum-information-processing protocols necessitates approximate, yet analytic descriptions that are valid for more strongly coupled qubit-resonator systems. Here we present a simple theoretical technique, using a basis of dressed states, to perturbatively account for the leading-order corrections to the RWA. By comparison with exact numerical results, we demonstrate that the method is accurate for moderately strong coupling, and provides a useful theoretical tool for describing fast quantum information processing. The method applies to any quantum two-level system linearly coupled to a harmonic oscillator or single-mode boson field.

quant-ph↗

Thermodynamic Equivalence of Certain Ideal Bose and Fermi Gases

We show that the recently discovered thermodynamic equivalence between noninteracting Bose and Fermi gases in two dimensions, and between one-dimensional Bose and Fermi systems with linear dispersion, both in the grand-canonical ensemble, are special cases of a larger class of equivalences of noninteracting systems having an energy-independent single-particle density of states. We also conjecture that the same equivalence will hold in the grand-canonical ensemble for any noninteracting quantum gas with a discrete ladder-type spectrum whenever $σΔ/ N k_{\rm B} T$ is small, where $N$ is the average particle number and $σ$ its standard deviation, $Δ$ is the level spacing, $k_{\rm B}$ is Boltzmann's constant, and $T$ is the temperature.

cond-mat.stat-mech↗