arXiv subjects

Alec Maassen van den Brink

Publications and source records attributed to Alec Maassen van den Brink.

36 records · Page 2Linked to original sources

arXiv2003

Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit

Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a _continuously_ observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of_Rabi spectroscopy_ enabled a long coherence time of about 2.5 microseconds, corresponding to an effective qubit quality factor \~7000.

cond-mat.mes-hall↗

arXiv2003

Approach to the extremal limit of the Schwarzschild-de Sitter black hole

The quasinormal-mode spectrum of the Schwarzschild-de Sitter black hole is studied in the limit of near-equal black-hole and cosmological radii. It is found that the mode_frequencies_ agree with the P"oschl-Teller approximation to one more order than previously realized, even though the effective_potential_ does not. Whether the spectrum approaches the limiting one uniformly in the mode index is seen to depend on the chosen units (to the order investigated). A perturbation framework is set up, in which these issues can be studied to higher order in future.

gr-qc↗

arXiv2003

Unconventional Gravitational Excitation of a Schwarzschild Black Hole

Besides the well-known quasinormal modes, the gravitational spectrum of a Schwarzschild black hole also has a continuum part on the negative imaginary frequency axis. The latter is studied numerically for quadrupole waves. The results show unexpected striking behavior near the algebraically special frequency $Ω=-4i$. This reveals a pair of unconventional damped modes very near $Ω$, confirmed analytically.

gr-qc↗

arXiv2003

Tunable coupling of superconducting qubits

We study an LC-circuit implemented using a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias current, the junction can be tuned in and out of resonance and entangled with the qubits coupled to it. One can thus implement two-qubit operations by mediating entanglement. We consider the examples of CBJJ and charge--phase qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit designs.

cond-mat.mes-hall↗

arXiv2003

Josephson-phase qubit without tunneling

We show that a complete set of one-bit gates can be realized by coupling the two logical states of a phase qubit to a third level (at higher energy) using microwave pulses. Thus, one can achieve coherent control without invoking any tunneling between the qubit levels. We propose two implementations, using rf-SQUIDs and d-wave Josephson junctions.

cond-mat.mes-hall↗

arXiv2003

Comment on `Aharonov--Casher-Effect Suppression of Macroscopic Tunneling of Magnetic Flux'

A recent Letter [1] has proposed a device, consisting of an rf SQUID with the junction replaced by a double one, i.e. a Bloch transistor. For symmetric Josephson couplings, and for specific flux bias and gate voltage applied to the transistor's island, the tunneling of encircled flux between its two local potential minima is claimed to be suppressed completely due to destructive interference. This comment purports to show that this claim in general is not valid. Namely, the very Hamiltonian (1) in [1], from which the effect is derived, describes the circuit only under an additional condition. [1] J.R. Friedman and D.V. Averin, Phys. Rev. Lett._88_, 050403 (2002).

cond-mat.mes-hall↗

arXiv2002

Low-frequency characterization of quantum tunneling in flux qubits

We propose to investigate flux qubits by the impedance measurement technique (IMT), currently used to determine the current--phase relation in Josephson junctions. We analyze in detail the case of a high-quality tank circuit coupled to a persistent-current qubit, to which IMT was successfully applied in the classical regime. It is shown that low-frequency IMT can give considerable information about the level anticrossing, in particular the value of the tunneling amplitude. An interesting difference exists between applying the ac bias directly to the tank and indirectly via the qubit. In the latter case, a convenient way to find the degeneracy point in situ is described. Our design only involves existing technology, and its noise tolerance is quantitatively estimated to be realistic.

cond-mat.supr-con↗

arXiv2002

Liouville invariance in quantum and classical mechanics

The density-matrix and Heisenberg formulations of quantum mechanics follow--for unitary evolution--directy from the Schr"odinger equation. Nevertheless, the symmetries of the corresponding evolution operator, the Liouvillian L=i[.,H], need not be limited to those of the Hamiltonian H. This is due to L only involving eigenenergy_differences_, which can be degenerate even if the energies themselves are not. Remarkably, this possibility has rarely been mentioned in the literature, and never pursued more generally. We consider an example involving mesoscopic Josephson devices, but the analysis only assumes familiarity with basic quantum mechanics. Subsequently, such _L-symmetries_ are shown to occur more widely, in particular also in classical mechanics. The symmetry's relevance to dissipative systems and quantum-information processing is briefly discussed.

quant-ph↗

arXiv2002

Book review of Z. Haba, Feynman Integral and Random Dynamics in Quantum Physics

The book deals with a stochastic formulation of path integration in real time, by rotating the_space_ variables over exp(i pi/4). Preliminary chapters deal with quantum and classical mechanics, probability theory and stochastic calculus, and the conventional approach to path integration through the Trotter product formula. Subsequently, the stochastic formulation in complex space is established, and applied to semi-classical expansions, nonlinear oscillations, quantum dynamics on analytic manifolds, dissipative systems (i.e., those which are open in that they interact with an environment), tunneling, field theory, and computer simulations.

quant-ph↗

arXiv2001

Comments on `Stable Quantum Computation of Unstable Classical Chaos,' `Efficient Quantum Computing Insensitive to Phase Errors,' and `Quantum Computer Inverting Time Arrow for Macroscopic Systems'

Recently, the paper B. Georgeot and D.L. Shepelyansky, Phys. Rev. Lett._86_, 5393 (2001) has been criticized [C. Zalka, quant-ph/0110019; L. Di'osi, quant-ph/0110026]. The Letter claims an exponential speedup and reduction in error sensitivity, when phase-space density evolution under the Arnold cat map is performed on a quantum computer. On the one hand, some points have not yet been made by previous respondents. On the other, the authors' reaction [quant-ph/0110142] raises new issues. The present note addresses both.

quant-ph↗

arXiv2000

SUSY Transformations for Quasinormal Modes of Open Systems

Supersymmetry (SUSY) in quantum mechanics is extended from square-integrable states to those satisfying the outgoing-wave boundary condition, in a Klein-Gordon formulation. This boundary condition allows both the usual normal modes and quasinormal modes with complex eigenvalues. The simple generalization leads to three features: the counting of eigenstates under SUSY becomes more systematic; the linear-space structure of outgoing waves (nontrivially different from the usual Hilbert space of square-integrable states) is preserved by SUSY; and multiple states at the same frequency (not allowed for normal modes) are also preserved. The existence or otherwise of SUSY partners is furthermore relevant to the question of inversion: are open systems uniquely determined by their complex outgoing-wave spectra?

math-ph↗

arXiv2000

Quantum-efficient charge detection using a single-electron transistor

We evaluate the detector nonideality (and energy sensitivity) of a normal-state single-electron transistor (SET) in the cotunneling regime in a two-charge-state approximation. For small conductances and at zero temperature, the SET's performance as a charge-qubit readout device is characterized by a universal one-parameter function. The result shows that near-ideal, quantum-limited measurement is possible for a wide range of small bias voltages. However, near the threshold voltage for crossover to sequential tunneling, the device becomes strongly nonideal. The (symmetrized) current-charge cross-correlation vanishes for low frequencies, causing two different definitions of detector nonideality to agree. Interpretations of these findings are discussed.

cond-mat.mes-hall↗

arXiv2000

Analytic treatment of black-hole gravitational waves at the algebraically special frequency

We study the Regge-Wheeler and Zerilli equations (RWE and ZE) at the `algebraically special frequency' $Ω$, where these equations admit an exact solution (elaborated here), generating the SUSY relationship between them. The physical significance of the SUSY generator and of the solutions at $Ω$ in general is elucidated as follows. The RWE has no (quasinormal or total-transmission) modes at all; however, $Ω$ is nonetheless `special' in that (a) for the outgoing wave into the horizon one has a `miraculous' cancellation of a divergence expected due to the exponential potential tail, and (b) the branch-cut discontinuity at $ω=Ω$ vanishes in the outgoing wave to infinity. Moreover, (a) and (b) are related. For the ZE, its only mode is the-inverse-SUSY generator, which is at the same time a quasinormal mode_and_ a total-transmission mode propagating to infinity. The subtlety of these findings (of general relevance for future study of the equations on or near the negative imaginary $ω$-axis) may help explain why the situation has sometimes been controversial. For finite black-hole rotation, the algebraically special modes are shown to be totally transmitting, and the implied singular nature of the Schwarzschild limit is clarified. The analysis draws on a recent detailed investigation of SUSY in open systems [math-ph/9909030].

gr-qc↗

arXiv1999

SUSY Transformations for Quasinormal and Total-Transmission Modes of Open Systems

Quasinormal modes are the counterparts in open systems of normal modes in conservative systems; defined by outgoing-wave boundary conditions, they have complex eigenvalues. The conditions are studied for a system to have a supersymmetric(SUSY) partner with the same complex quasinormal-mode spectrum (or the same except for one eigenvalue). The discussion naturally includes total-transmission modes as well(incoming at one extreme and outgoing at the other). Several types of SUSY transformations emerge, and each is illustrated with examples, including the transformation among different Poschl-Teller potentials and the well-known identity in spectrum between the two parity sectors of linearized gravitational waves propagating on a Schwarzschild background. In contrast to the case of normal modes, there may be multiple essentially isospectral partners, each missing a different state. The SUSY transformation preserves orthonormality under a bilinear map which is the analog of the usual inner product for conservative systems. SUSY transformations can lead to doubled quasinormal and total-transmission modes; this phenomenon is analysed and illustrated. The existence or otherwise of SUSY partners is also relevant to the question of inversion: are open wave systems uniquely determined by their complex spectra?

math-ph↗

arXiv1999

Jordan blocks and generalized bi-orthogonal bases: realizations in open wave systems

Dissipative systems can be described in terms of non-hermitian hamiltonians H, whose left eigenvectors f^j and right eigenvectors f_j form a bi-orthogonal system. Bi-orthogonal systems could suffer from two difficulties. (a) If the eigenvectors do not span the whole space, then H can only be diagonalized to blocks (the Jordan-block problem). (b) Normalization would not be possible and many familiar-looking formulas would fail if (f^j,f_j) = 0 for some j (the orthonormalization problem). Waves in open systems provide a well-founded realization of a bi-orthogonal system, and it is shown that these two problems can indeed occur and are both related to higher-order poles in the frequency-domain Green's function. The resolution is then given by introducing a generalized duality transformation involving extra basis vectors, whose time evolution is modified by polynomials in the time t. One thus obtains a nontrivial extension of the bi-orthogonal formalism for dissipative systems.

math-ph↗

arXiv1999

Exactly solvable path integral for open cavities in terms of quasinormal modes

We evaluate the finite-temperature Euclidean phase-space path integral for the generating functional of a scalar field inside a leaky cavity. Provided the source is confined to the cavity, one can first of all integrate out the fields on the outside to obtain an effective action for the cavity alone. Subsequently, one uses an expansion of the cavity field in terms of its quasinormal modes (QNMs)-the exact, exponentially damped eigenstates of the classical evolution operator, which previously have been shown to be complete for a large class of models. Dissipation causes the effective cavity action to be nondiagonal in the QNM basis. The inversion of this action matrix inherent in the Gaussian path integral to obtain the generating functional is therefore nontrivial, but can be accomplished by invoking a novel QNM sum rule. The results are consistent with those obtained previously using canonical quantization.

quant-ph↗

arXiv1998

Second-quantization of open systems using quasinormal modes

The second-quantization of a scalar field in an open cavity is formulated, from first principles, in terms of the quasinormal modes (QNMs), which are the eigensolutions of the evolution equation that decay exponentially in time as energy leaks to the outside. This formulation provides a description involving the cavity degrees of freedom only, with the outside acting as a (thermal or driven) source. Thermal correlation functions and cavity Feynman propagators are thus expressed in terms of the QNMs, labeled by a discrete index rather than a continuous momentum. Single-resonance domination of the density of states and the spontaneous decay rate is then given a proper foundation. This is a first essential step towards the application of QNMs to cavity QED phenomena, to be reported elsewhere.

quant-ph↗

arXiv1994

Temperature relaxation and the Kapitza boundary resistance paradox

The calculation of the Kapitza boundary resistance between dissimilar harmonic solids has since long (Little [Can. J. Phys. 37, 334 (1959)]) suffered from a paradox: this resistance erroneously tends to a finite value in the limit of identical solids. We resolve this paradox by calculating temperature differences in the final heat-transporting state, rather than with respect to the initial state of local equilibrium. For a one-dimensional model we thus derive an exact, paradox-free formula for the boundary resistance. The analogy to ballistic electron transport is explained.

cond-mat↗