arXiv subjects

Alexander Shnirman

Publications and source records attributed to Alexander Shnirman.

108 records · Page 6Linked to original sources

arXiv2004

Ground state cooling of mechanical resonators

We propose an application of a single Cooper pair box (Josephson qubit) for active cooling of nanomechanical resonators. Latest experiments with Josephson qubits demonstrated that long coherence time of the order of microsecond can be achieved in special symmetry points. Here we show that this level of coherence is sufficient to perform an analog of the well known in quantum optics ``laser'' cooling of a nanomechanical resonator capacitively coupled to the qubit. By applying an AC driving to the qubit or the resonator, resonators with frequency of order 100 MHz and quality factors higher than $10^3$ can be efficiently cooled down to their ground state, while lower frequency resonators can be cooled down to micro-Kelvin temperatures. We also consider an alternative setup where DC-voltage-induced Josephson oscillations play the role of the AC driving and show that cooling is possible in this case as well.

cond-mat.mes-hall↗

arXiv2003

Dephasing of solid-state qubits at optimal points

Motivated by recent experiments with Josephson-junction circuits, we analyze the influence of various noise sources on the dynamics of two-level systems at optimal operation points where the linear coupling to low-frequency fluctuations is suppressed. We study the decoherence due to nonlinear (quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic noise power spectra. For 1/f noise strong higher-order effects influence the evolution.

cond-mat.mes-hall↗

arXiv2003

Dephasing of qubits by transverse low-frequency noise

We analyze the dissipative dynamics of a two-level quantum system subject to low-frequency, e.g. 1/f noise, motivated by recent experiments with superconducting quantum circuits. We show that the effect of transverse linear coupling of the system to low-frequency noise is equivalent to that of quadratic longitudinal coupling. We further find the decay law of quantum coherent oscillations under the influence of both low- and high-frequency fluctuations, in particular, for the case of comparable rates of relaxation and pure dephasing.

cond-mat.mes-hall↗

arXiv2003

Quantum Zeno effect in the Cooper-pair transport through a double-island Josephson system

Motivated by recent experiments, we analyze transport of Cooper pairs through a double-island Josephson qubit. At low bias in a certain range of gate voltages coherent superpositions of charge states play a crucial role. Analysis of the evolution of the density matrix allows us to cover a wide range of parameters, incl. situations with degenerate levels, when dissipation strongly affects the coherent eigenstates. At high noise levels the so-called Zeno effect can be observed, which slows down the transport. Our analysis explains certain features of the I-V curves, in particular the visibility and shape of resonant peaks and lines.

cond-mat.mes-hall↗

arXiv2003

Dissipation in Josephson qubits

We discuss the dissipative dynamics of superconducting qubits in the applicability range of the Bloch equations and beyond.

cond-mat.mes-hall↗

arXiv2003

Spin-spin correlators in Majorana representation

In the Majorana representation of a spin 1/2 we find an identity which relates spin-spin correlators to one-particle fermionic correlators. This should be contrasted with the straightforward approach in which two-particle (four-fermion) correlators need to be calculated. We discuss applications to the analysis of the dynamics of a spin coupled to a dissipative environment and of a quantum detector performing a continuous measurement of a qubit's state.

cond-mat.mes-hall↗

arXiv2002

Dephasing and Renormalization in Quantum Two-Level Systems

Motivated by fundamental questions about the loss of phase coherence at low temperature we consider relaxation, dephasing and renormalization effects in quantum two-level systems which are coupled to a dissipative environment. We observe that experimental conditions, e.g., details of the initial state preparation, determine to which extent the environment leads to dephasing or to renormalization effects. We analyze an exactly solvable limit where the relation between both can be demonstrated explicitly. We also study the effects of dephasing and renormalization on response functions.

cond-mat.mes-hall↗

arXiv2002

Noise and decoherence in quantum two-level systems

Motivated by recent experiments with Josephson-junction circuits we reconsider decoherence effects in quantum two-level systems (TLS). On one hand, the experiments demonstrate the importance of 1/f noise, on the other hand, by operating at symmetry points one can suppress noise effects in linear order. We, therefore, analyze noise sources with a variety of power spectra, with linear or quadratic coupling, which are longitudinal or transverse relative to the eigenbasis of the unperturbed Hamiltonian. To evaluate the dephasing time for transverse 1/f noise second-order contributions have to be taken into account. Manipulations of the quantum state of the TLS define characteristic time scales. We discuss the consequences for relaxation and dephasing processes.

cond-mat.mes-hall↗

arXiv2000

Quantum state engineering with Josephson-junction devices

We review recent theoretical and experimental progress in quantum state engineering with Josephson junction devices. The concepts of quantum computing have stimulated an increased activity in the field. Either charges or phases (fluxes) of the Josephson systems can be used as quantum degrees of freedom, and their quantum state can be manipulated coherently by voltage and current pulses. They thus can serve as qubits, and quantum logic gates can be performed. Their phase coherence time, which is limited, e.g., by the electromagnetic fluctuations in the control circuit, is long enough to allow a series of these manipulations. The quantum measurement process performed by a single-electron transistor, a SQUID, or further nanoelectronic devices is analyzed in detail.

cond-mat.mes-hall↗

arXiv2000

Statistics and noise in a quantum measurement process

The quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit is studied. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong measurement and expect this description to apply for a wide class of quantum measurements. We derive the probability distributions for the current and charge in different stages of the process. In the parameter regime of the strong measurement the current develops a telegraph-noise behavior which can be detected in the noise spectrum.

cond-mat.mes-hall↗

arXiv1999

Nano-electronic Realizations of Quantum Bits

Quantum computers could perform certain tasks which no classical computer can perform in acceptable times. Josephson junction circuits can serve as building blocks of quantum computers. We discuss and compare two designs, which employ charge or magnetic flux degrees of freedom to process quantum information. In both cases, elementary single-qubit and two-qubit logic gates can be performed by voltage or flux pulses. The coherence time is long enough to allow a series of such operations. We also discuss the read-out, i.e., a quantum measurement process. In the charge case it is accomplished by coupling a single-electron transistor to the qubit.

cond-mat.mes-hall↗

arXiv1999

Josephson-Junction Qubits and the Readout Process by Single-Electron Transistors

Several physical realizations of quantum bits have been proposed. Of those, nano-electronic devices appear most suitable for large-scale integration and potential applications. We suggest to use low-capacitance Josephson junctions, exploiting the coherence of tunneling in the superconducting state combined with the possibility to control individual charges by Coulomb blockade effects (cond-mat/9706016,cond-mat/9808067). These systems constitute quantum bits, with logical states differing by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. In addition to the manipulation of qubits the resulting quantum state has to be read out. This can be accomplished by coupling a single-electron transistor capacitively to the qubit (cond-mat/9801125). To describe this quantum measurement process we study the time evolution of the density matrix of the coupled system. Only when a transport voltage is turned on, the transistor destroys the phase coherence of the qubit; in this case within a short time. The measurement is accomplished after a longer time scale, when the signal resolves the different quantum states. At still longer times the measurement process itself destroys the information about the initial state. We present a suitable set of system parameters, which can be realized by present-day technology.

cond-mat.mes-hall↗

arXiv1999

Low-energy quasiparticle states near extended scatterers in d-wave superconductors and their connection with SUSY quantum mechanics

Low-energy quasiparticle states, arising from scattering by single-particle potentials in d-wave superconductors, are addressed. Via a natural extension of the Andreev approximation, the idea that sign-variations in the superconducting pair-potential lead to such states is extended beyond its original setting of boundary scattering to the broader context of scattering by general single-particle potentials, such as those due to impurities. The index-theoretic origin of these states is exhibited via a simple connection with Witten's supersymmetric quantum-mechanical model.

cond-mat.supr-con↗

arXiv1999

Resonant states and order-parameter suppression near point-like impurities in d-wave superconductors

We examine the role of order-parameter suppression in the development of low-energy peaks (i.e., resonances) in the tunneling density of states near a non-magnetic impurity in a d-wave superconductor. Without order-parameter suppression, the zero-energy resonance appears only in the unitary (i.e., strong impurity) limit. However, suppression makes the resonance appear even when the impurity is much weaker. To model this situation, we make the physical hypothesis that the order parameter is reduced whenever one electron of a Cooper pair encounters the impurity, a hypothesis that retains the exact solvability of the problem. In this way, we determine that suppression of the order parameter drives the effective strength of the impurity towards the unitary limit. We determine the order-parameter reduction variationally, and show that the ratios between the main energy scales--the band width and superconducting gap--strongly affect this reduction and, in consequence, the position and width of the resonance.

cond-mat.supr-con↗

arXiv1998

Josephson-Junction Qubits with Controlled Couplings

Low-capacitance Josephson junctions, where Cooper pairs tunnel coherently while Coulomb blockade effects allow the control of the total charge, provide physical realizations of quantum bits (qubits), with logical states differing by one Cooper-pair charge on an island. The single- and two-bit operations required for quantum computation can be performed by applying a sequence of gate voltages. A basic design, described earlier [cond-mat/9706016], is sufficient to demonstrate the principles, but requires a high precision time control, and residual two-bit interactions introduce errors. Here we suggest a new nano-electronic design, close to ideal, where the Josephson junctions are replaced by controllable SQUIDs. This relaxes the requirements on the time control and system parameters substantially, and the two-bit coupling can be switched exactly between zero and a non-zero value for arbitrary pairs. The phase coherence time is sufficiently long to allow a series of operations.

cond-mat.mes-hall↗

arXiv1998

Quantum Measurements Performed with a Single-Electron Transistor

Low-capacitance Josephson junction systems as well as coupled quantum dots, in a parameter range where single charges can be controlled, provide physical realizations of quantum bits, discussed in connection with quantum computing. The necessary manipulation of the quantum states can be controlled by applied gate voltages. In addition, the state of the system has to be read out. Here we suggest to measure the quantum state by coupling a single-electron transistor to the q-bit. As long as no transport voltage is applied, the transistor influences the quantum dynamics of the q-bit only weakly. We have analyzed the time evolution of the density matrix of the transistor and q-bit when a voltage is turned on. For values of the capacitances and temperatures which can be realized by modern nano-techniques the process constitutes a quantum measurement process.

cond-mat.mes-hall↗

arXiv1997

Quantum Manipulations of Small Josephson Junctions

Low-capacitance Josephson junction arrays in the parameter range where single charges can be controlled are suggested as possible physical realizations of the elements which have been considered in the context of quantum computers. We discuss single and multiple quantum bit systems. The systems are controlled by applied gate voltages, which also allow the necessary manipulation of the quantum states. We estimate that the phase coherence time is sufficiently long for experimental demonstration of the principles of quantum computation.

cond-mat.mes-hall↗

arXiv1996

Integer and fractional charge solitons in modulated strips in the fractional quantum Hall regime

We propose the existence and study the solitonic excitations in two kinds of samples in the fractional quantum Hall regime. One is a strip modulated by a one-dimensional array of gates. The other is made of two parallel strips coupled by a one-dimensional array of tunnel barriers. We predict the existence of integer charge solitons in the first case, and fractional charge solitons in the second case. We study the two cases both in the dissipative and in the inertial limits.

cond-mat↗