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G. P. Berman

Publications and source records attributed to G. P. Berman.

At least 55 records · Page 3Linked to original sources
arXiv2005

Implementation of quantum logic operations and creation of entanglement in a silicon-based quantum computer with constant interaction

We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear-electron hyperfine and electron-electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Control-Not gate. The exchange interaction is constant and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented by rectangular radio-frequency pulses. This architecture is scalable and does not require manufacturing nanoscale electronic gates. As shown in this paper parameters of a quantum protocol can be derived analytically even for a computer with a large number of qubits using our perturbation approach. We present the protocol for initialization of the nuclear spins and the protocol for creation of entanglement. All analytical results are tested numerically using a two-qubit system.

quant-ph↗
arXiv2005

Coherent effects in magneto-transport through Zeeman split levels

We study non-equilibrium electronic transport through a quantum dot or impurity weakly coupled to ferromagnetic leads. Based on the rate equation formalism we derive noise spectra for the transport current. We show that due to quantum interference between different spin components of the current the spectrum develops a peak or a dip at the frequency corresponding to Zeeman splitting in the quantum dot. The detailed analysis of the spectral structure of the current is carried out for noninteracting electrons as well as in the regime of Coulomb blockade.

cond-mat.mes-hall↗
arXiv2005

Frequency shift in the oscillating cantilever-driven adiabatic reversals technique as a function of the spin location

The theory of the oscillating cantilever-driven adiabatic reversals (OSCAR) in magnetic resonance force microscopy (MRFM) is extended to describe the relation between an external magnetic field and a dipole magnetic field for an arbitrary location of the single spin. An analytical estimate for the OSCAR MRFM frequency shift is derived and shown to be in excellent agreement with numerical simulations. The dependence of the frequency shift on the position of the spin relative to the cantilever has characteristic maxima and minima which can be used to determine the spin location experimentally.

cond-mat.other↗
arXiv2005

Sub Shot-Noise Phase Sensitivity with a Bose-Einstein Condensate Mach-Zehnder Interferometer

Bose Einstein Condensates, with their coherence properties, have attracted wide interest for their possible application to ultra precise interferometry and ultra weak force sensors. Since condensates, unlike photons, are interacting, they may permit the realization of specific quantum states needed as input of an interferometer to approach the Heisenberg limit, the supposed lower bound to precision phase measurements. To this end, we study the sensitivity to external weak perturbations of a representative matter-wave Mach-Zehnder interferometer whose input are two Bose-Einstein condensates created by splitting a single condensate in two parts. The interferometric phase sensitivity depends on the specific quantum state created with the two condensates, and, therefore, on the time scale of the splitting process. We identify three different regimes, characterized by a phase sensitivity $Δθ$ scaling with the total number of condensate particles $N$ as i) the standard quantum limit $Δθ\sim 1/N^{1/2}$, ii) the sub shot-noise $Δθ\sim 1/N^{3/4}$ and the iii) the Heisenberg limit $Δθ\sim 1/N$. However, in a realistic dynamical BEC splitting, the 1/N limit requires a long adiabaticity time scale, which is hardly reachable experimentally. On the other hand, the sub shot-noise sensitivity $Δθ\sim 1/N^{3/4}$ can be reached in a realistic experimental setting. We also show that the $1/N^{3/4}$ scaling is a rigorous upper bound in the limit $N \to \infty$, while keeping constant all different parameters of the bosonic Mach-Zehnder interferometer.

cond-mat.other↗
arXiv2005

Single qubit measurements with an asymmetric single-electron transistor

We investigate qubit measurements using a single electron transistor (SET). Applying the Schrödinger equation to the entire system we find that an asymmetric SET is considerably more efficient than a symmetric SET. The asymmetric SET becomes close to an ideal detector in the large asymmetry limit. We also compared the SET detector with a point-contact detector. This comparison allows us to illuminate the relation between information gain in the measurement process and the decoherence generated by these measurement devices.

cond-mat.mes-hall↗
arXiv2005

Quantum Signatures of The Classical Disconnection Border

A quantum Heisenberg model with anisotropic coupling and all-to-all interaction has been analyzed using the Bose-Einstein statistics. In Ref.\cite{jsp} the existence of a classical energy disconnection border (EDB) in the same kind of models has been demonstrated. We address here the problem to find quantum signatures of the EDB. An independent definition of a quantum disconnection border, motivated by considerations strictly valid in the quantum regime is given. We also discuss the dynamical relevance of the quantum border with respect to quantum magnetic reversal. Contrary to the classical case the magnetization can flip even below the EDB through Macroscopic Quantum Tunneling. We evaluate the time scale for magnetic reversal from statistical and spectral properties, for a small number of particles and in the semiclassical limit.

cond-mat.other↗
arXiv2005

The Fermi-Pasta-Ulam problem: 50 years of progress

A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection with the problems of ergodicity, integrability, chaos and stability of motion. New directions related to the Bose-Einstein condensation and quantum systems of interacting Bose-particles are also considered.

nlin.CD↗
arXiv2005

Spin Diffusion and Relaxation in Solid State Spin Quantum Computer

The processes of spin diffusion and relaxation are studied theoretically and numerically for quantum computation applications. Two possible realizations of a spin quantum computer (SQC) are analyzed: (i) a boundary spin chain in a 2D spin array and (ii) an isolated spin chain. In both cases, spin diffusion and relaxation are caused by a fast relaxing spin located outside the SQC. We have shown that in both cases the relaxation can be suppressed by an external non-uniform magnetic field. In the second case, our computer simulations have revealed various types of relaxation processes including the excitation of a random distribution of magnetic moments and the formation of stationary and moving domain walls. The region of optimal parameters for suppression of rapid spin relaxation is discussed.

cond-mat.mtrl-sci↗
arXiv2005

Spin Diffusion and Relaxation in a Nonuniform Magnetic Field

We consider a quasiclassical model that allows us to simulate the process of spin diffusion and relaxation in the presence of a highly nonuniform magnetic field. The energy of the slow relaxing spins flows to the fast relaxing spins due to the dipole-dipole interaction between the spins. The magnetic field gradient suppresses spin diffusion and increases the overall relaxation time in the system. The results of our numerical simulations are in a good agreement with the available experimental data.

cond-mat.mtrl-sci↗
arXiv2004

Dephasing and breakdown of adiabaticity in the splitting of Bose Einstein Condensates

We study the quantum dynamics of a BEC condensate trapped in a double-well potential with a rising interwell barrier. We analytically find the characteristic time scales of the splitting process and compare our results with numerical analyses available in the literature. In first stage of the dynamics, the condensate follows adiabatically the rising of the interwell barrier. At a critical time $t_{ad}$, small amplitude fluctuations around the average trajectory increase exponentially fast, signaling the break-down of adiabaticity. We have found a highly non-trivial dependence of the dephasing time $t_D$, defined by $σ_ϕ(t_D)=1$, where $σ_ϕ(t)$ is the dynamical quantum phase spreading, on $t_{ad}$ and on the ramping time of the interwell barrier.

cond-mat.stat-mech↗
arXiv2004

Modeling and Simulations of a Single-Spin Measurement using MRFM

We review the quantum theory of a single spin magnetic resonance force microscopy (MRFM). We concentrate on the novel technique called oscillating cantilever-driven adiabatic reversals (OSCAR), which has been used for a single spin detection (Dan Rugar, Talk on the 2004 IEEE NTC Quantum Device Technology Workshop). First we describe the quantum dynamics of the cantilever-spin system using simple estimates in the spirit of the mean field approximation. Then we present the results of our computer simulations of the Schrodinger equation for the wave function of the cantilever-spin system and of the master equation for the density matrix of the system. We demonstrate that the cantilever behaves like a quasi-classical measurement device which detects the spin projection along the effective magnetic field. We show that the OSCAR technique provides continuous monitoring of the single spin, which could be used to detect the mysterious quantum collapses of the wave function of the cantilever-spin system.

quant-ph↗
arXiv2004

Quantum logic operations and creation of entanglement in a scalable superconducting quantum computer with long-range constant interaction between qubits

We consider a one-dimensional chain of many superconducting quantum interference devices (SQUIDs), serving as charge qubits. Each SQUID is coupled to its nearest neighbors through constant capacitances. We study the quantum logic operations and implementation of entanglement in this system. Arrays with two and three qubits are considered in detail. We show that the creation of entanglement with an arbitrary number of qubits can be implemented, without systematic errors, even when the coupling between qubits is not small. A relatively large coupling constant allows one to increase the clock speed of the quantum computer. We analytically and numerically demonstrate the creation of the entanglement for this case, which can be a good test for the experimental implementation of a relatively simple quantum protocol with many qubits. We discuss a possible application of our approach for implementing universal quantum logic for more complex algorithms by decreasing the coupling constant and, correspondingly, decreasing the clock speed. The errors introduced by the long-range interaction for the universal logic gates are estimated analytically and calculated numerically. Our results can be useful for experimental implementation of quantum algorithms using controlled magnetic fluxes and gate voltages applied to the SQUIDs. The algorithms discussed in this paper can be implemented using already existing technologies in superconducting systems with constant inter-qubit coupling.

cond-mat.supr-con↗
arXiv2004

Controlling the Spin Polarization of the Electron Current in a Semimagnetic Resonant-Tunneling Diode

The spin filtering effect of the electron current in a double-barrier resonant-tunneling diode (RTD) consisting of ZnMnSe semimagnetic layers has been studied theoretically. The influence of the distribution of the magnesium ions on the coefficient of the spin polarization of the electron current has been investigated. The dependence of the spin filtering degree of the electron current on the external magnetic field and the bias voltage has been obtained. The effect of the total spin polarization of the electron current has been predicted. This effect is characterized by total suppression of the spin-up component of electron current, that takes place when the Fermi level coincides with the lowest Landau level for spin-up electrons in the RTD semimagnetic emitter.

cond-mat.other↗
arXiv2004

Wave function collapses in a single spin magnetic resonance force microscopy

We study the effects of wave function collapses in the oscillating cantilever driven adiabatic reversals (OSCAR) magnetic resonance force microscopy (MRFM) technique. The quantum dynamics of the cantilever tip (CT) and the spin is analyzed and simulated taking into account the magnetic noise on the spin. The deviation of the spin from the direction of the effective magnetic field causes a measurable shift of the frequency of the CT oscillations. We show that the experimental study of this shift can reveal the information about the average time interval between the consecutive collapses of the wave function

quant-ph↗
arXiv2004

Double-Slit Interferometry with a Bose-Einstein Condensate

A Bose-Einstein "double-slit" interferometer has been recently realized experimentally by (Y. Shin et. al., Phys. Rev. Lett. 92 50405 (2004)). We analyze the interferometric steps by solving numerically the time-dependent Gross-Pitaevski equation in three-dimensional space. We focus on the adiabaticity time scales of the problem and on the creation of spurious collective excitations as a possible source of the strong dephasing observed experimentally. The role of quantum fluctuations is discussed.

cond-mat.soft↗
arXiv2004

Modeling full adder in Ising spin quantum computer with 1000 qubits using quantum maps

The quantum adder is an essential attribute of a quantum computer, just as classical adder is needed for operation of a digital computer. We model the quantum full adder as a realistic complex algorithm on a large number of qubits in an Ising-spin quantum computer. Our results are an important step toward effective modeling of the quantum modular adder which is needed for Shor's and other quantum algorithms. Our full adder has the following features: (i) The near-resonant transitions with small detunings are completely suppressed, which allows us to decrease errors by several orders of magnitude and to model a 1000-qubit full adder. (We add a 1000-bit number using 2001 spins.) (ii) We construct the full adder gates directly as sequences of radio-frequency pulses, rather than breaking them down into generalized logical gates, such as Control-Not and one qubit gates. This substantially reduces the number of pulses needed to implement the full adder. [The maximum number of pulses required to add one bit (F-gate) is 15]. (iii) Full adder is realized in a homogeneous spin chain. (iv) The phase error is minimized: the F-gates generate approximately the same phase for different states of the superposition. (v) Modeling of the full adder is performed using quantum maps instead of differential equations. This allows us to reduce the calculation time to a reasonable value.

quant-ph↗
arXiv2004

A Model for Quantum Jumps in Magnetic Resonance Force Microscopy

We propose a simple model which describes the statistical properties of quantum jumps in a single-spin measurement using the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. Our computer simulations based on this model predict the average time interval between two consecutive quantum jumps and the correlation time to be proportional to the characteristic time of the magnetic noise and inversely proportional to the square of the magnetic noise amplitude.

quant-ph↗