arXiv subjects

G. P. Berman

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

At least 73 records · Page 4Linked to original sources

arXiv2004

Survival of quantum effects for observables after decoherence

When a quantum nonlinear system is linearly coupled to an infinite bath of harmonic oscillators, quantum coherence of the system is lost on a decoherence time-scale $τ_D$. Nevertheless, quantum effects for observables may still survive environment-induced decoherence, and be observed for times much larger than the decoherence time-scale. In particular, we show that the Ehrenfest time, which characterizes a departure of quantum dynamics for observables from the corresponding classical dynamics, can be observed for a quasi-classical nonlinear oscillator for times $τ\ggτ_D$. We discuss this observation in relation to recent experiments on quantum nonlinear systems in the quasi-classical region of parameters.

quant-ph↗

arXiv2003

Analytic solutions for quantum logic gates and modeling pulse errors in a quantum computer with a Heisenberg interaction

We analyze analytically and numerically quantum logic gates in a one-dimensional spin chain with Heisenberg interaction. Analytic solutions for basic one-qubit gates and swap gate are obtained for a quantum computer based on logical qubits. We calculated the errors caused by imperfect pulses which implement the quantum logic gates. It is numerically demonstrated that the probability error is proportional to $ε^4$, while the phase error is proportional to $ε$, where $ε$ is the characteristic deviation from the perfect pulse duration.

quant-ph↗

arXiv2003

Irregular Dynamics in a One-Dimensional Bose System

We study many-body quantum dynamics of $δ$-interacting bosons confined in a one-dimensional ring. Main attention is payed to the transition from the mean-field to Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wavefunction and the momentum distribution depend on time for a weak and strong interactions. We show that the transition from regular (quasi-periodic) to irregular ("chaotic") dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.

cond-mat.stat-mech↗

arXiv2003

Regular and Random Magnetic Resonance Force Microscopy Signal with a Cantilever Oscillating Parallel to a Sample Surface

We study theoretically the magnetic resonance force microscopy (MRFM) in oscillating cantilever-driven adiabatic reversals (OSCAR) technique, for the case when the cantilever tip oscillates parallel to the surface of a sample. The main contribution to the MRFM signal is associated with a part of the resonance slice near the surface of the sample. The regular (approximately exponential) decay of the MRFM signal is followed by the non-dissipating random signal. The Fourier spectrum of the random signal has a characteristic peak which can be used for the identification of the signal.

cond-mat↗

arXiv2003

Minimization of nonresonant effects in a scalable Ising spin quantum computer

The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between neighboring spins. Selective excitations of the spins are enabled by a uniform gradient of the external magnetic field. We calculate the probabilities of all unwanted nonresonant transitions associated with the flip of each spin with nonresonant frequency and with flips of two spins: one with resonant and one with nonresonant frequencies. It is shown that these errors oscillate with changing the gradient of the external magnetic field. Choosing the optimal values of this gradient allows us to decrease these errors by 50%.

quant-ph↗

arXiv2003

Effects of electrostatic fields and Casimir force on cantilever vibrations

The effect of an external bias voltage and fluctuating electromagnetic fields on both the fundamental frequency and damping of cantilever vibrations is considered. An external voltage induces surface charges causing cantilever-sample electrostatic attraction. A similar effect arises from charged defects in dielectrics that cause spatial fluctuations of electrostatic fields. The cantilever motion results in charge displacements giving rise to Joule losses and damping. It is shown that the dissipation increases with decreasing conductivity and thickness of the substrate, a result that is potentially useful for sample diagnostics. Fluctuating electromagnetic fields between the two surfaces also induce attractive (Casimir) forces. It is shown that the shift in the cantilever fundamental frequency due to the Casimir force is close to the shift observed in recent experiments of Stipe et al. Both the electrostatic and Casimir forces have a strong effect on the cantilever eigenfrequencies, and both effects depend on the geometry of the cantilever tip. We consider cylindrical, spherical, and ellipsoidal tips moving parallel to a flat sample surface. The dependence of the cantilever effective mass and vibrational frequencies on the geometry of the tip is studied both numerically and analytically.

cond-mat↗

arXiv2003

Reduction of Magnetic Noise in Magnetic Resonance Force Microscopy

We study the opportunity to reduce a magnetic noise produced by a uniform cantilever with a ferromagnetic particle in magnetic resonance force microscopy (MRFM) applications. We demonstrate theoretically a significant reduction of magnetic noise and the corresponding increase of the MRFM relaxation time using a nonuniform cantilever.

cond-mat↗

arXiv2003

Neutral Radical Molecules Ordered in Self-Assembled Monolayer Systems for Quantum Information Processing

Implementation of quantum information processing based on spatially localized electronic spins in stable molecular radicals is discussed. The necessary operating conditions for such molecules are formulated in self-assembled monolayer (SAM) systems. As a model system we start with 1, 3 -diketone types of neutral radicals. Using first principles quantum chemical calculations we prove that these molecules have the stable localized electron spin, which may represent a qubit in quantum information processing.

quant-ph↗

arXiv2003

Relaxation and Zeno effect in qubit measurements

We consider a qubit interacting with its environment and continuously monitored by a detector represented by a point contact. Bloch-type equations describing the entire system of the qubit, the environment and the detector are derived. Using these equations we evaluate the detector current and its noise spectrum in terms of the decoherence and relaxation rates of the qubit. Simple expressions are obtained that show how these quantities can be accurately measured. We demonstrate that due to interaction with the environment, the measurement can never localize a qubit even for infinite decoherence rate.

cond-mat↗

arXiv2003

Quantum Dynamics of the Oscillating Cantilever-Driven Adiabatic Reversals in Magnetic Resonance Force Microscopy

We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We estimated the frequency shift of the cantilever vibrations and demonstrated that this shift causes the formation of a Schrodinger cat state which has some similarities and differences from the conventional MRFM technique which uses cyclic adiabatic reversals of spins. The interaction of the cantilever with the environment is shown to quickly destroy the coherence between the two possible cantilever trajectories. We have shown that using partial adiabatic reversals, one can produce a significant increase in the OSCAR signal.

quant-ph↗

arXiv2003

Random Spin Signal in Magnetic Resonance Force Microscopy

We study a random magnetic resonance force microscopy (MRFM) signal caused by the thermal vibrations of high frequency cantilever modes in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We show that the regular MRFM signal with a characteristic decay time, $τ_m$, is followed by a non-dissipative random signal with a characteristic time $τ_r$. We present the estimates for the values of $τ_m$ and $τ_r$. We argue that this random MRFM signal can be used for spin detection. It has a ``signature'' of a sharp peak in its Fourier spectrum.

cond-mat↗

arXiv2003

Spin Relaxation Caused by Thermal Excitations of High Frequency Modes of Cantilever Vibrations

We consider the process of spin relaxation in the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. We simulated the spin relaxation caused by thermal excitations of the high frequency cantilever modes in the region of the Rabi frequency of the spin sub-system. The minimum relaxation time obtained in our simulations is greater but of the same order of magnitude as one measured in recent experiments. We demonstrated that using a cantilever with nonuniform cross-sectional area may significantly increase spin relaxation time.

quant-ph↗

arXiv2002

Method for implementation of universal quantum logic gates in a scalable Ising spin quantum computer

We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising interaction between the neighboring spins. The selective excitations of the spins are provided by the gradient of the external magnetic field. The protocols are built of rectangular radio-frequency pulses. The phase and probability errors caused by unwanted transitions are minimized and computed numerically.

quant-ph↗

arXiv2002

Interference effects in resonant magneto-transport

We study non-equilibrium magneto-transport through a single electron transistor or an impurity. We find that due to spin-flip transitions, generated by the spin-orbit interaction, the spectral density of the tunneling current fluctuations develops a distinct peak at the frequency of Zeeman splitting. This mechanism explains modulation in the tunneling current at the Larmor frequency observed in scanning tunneling microscope (STM) experiments and can be utilized as a detector for single spin measurement.

cond-mat↗

arXiv2002

Single-Spin Measurement and Decoherence in Magnetic Resonance Force Microscopy

We consider a simple version of a cyclic adiabatic inversion (CAI) technique in magnetic resonance force microscopy (MRFM). We study the problem: What component of the spin is measured in the CAI MRFM? We show that the non-destructive detection of the cantilever vibrations provides a measurement of the spin component along the effective magnetic field. This result is based on numerical simulations of the Hamiltonian dynamics (the Schrodinger equation) and the numerical solution of the master equation.

quant-ph↗

arXiv2002

Transient Dynamics in Magnetic Force Microscopy for a Single-Spin Measurement

We analyze a single-spin measurement using a transient process in magnetic force microscopy (MFM) which could increase the maximum operating temperature by a factor of Q (the quality factor of the cantilever) in comparison with the static Stern-Gerlach effect. We obtain an exact solution of the master equation, which confirms this result. We also discuss the conditions required to create a macroscopic Schrodinger cat state in the cantilever.

quant-ph↗

arXiv2002

Dynamical fidelity of a solid-state quantum computation

In this paper we analyze the dynamics in a spin-model of quantum computer. Main attention is paid to the dynamical fidelity (associated with dynamical errors) of an algorithm that allows to create an entangled state for remote qubits. We show that in the regime of selective resonant excitations of qubits there is no any danger of quantum chaos. Moreover, in this regime a modified perturbation theory gives an adequate description of the dynamics of the system. Our approach allows to explicitly describe all peculiarities of the evolution of the system under time-dependent pulses corresponding to a quantum protocol. Specifically, we analyze, both analytically and numerically, how the fidelity decreases in dependence on the model parameters.

quant-ph↗

arXiv2002

Stationary cantilever vibrations in the oscillating cantilever-driven adiabatic reversals -- magnetic resonance force microscopy technique

We consider theoretically the novel technique in magnetic resonance force microscopy which is called ``oscillating cantilever-driven adiabatic reversals''. We present analytical and numerical analysis for the stationary cantilever vibrations in this technique. For reasonable values of parameters we estimate the resonant frequency shift as 6Hz per the Bohr magneton. We analyze also the regime of small oscillations of the paramagnetic moment near the transversal plane and the frequency shift of the damped cantilever vibrations.

quant-ph↗