Dynamics of a Magnetic Needle Magnetometer: Sensitivity to Landau-Lifshitz-Gilbert Damping.

An analysis of a single-domain magnetic needle (MN) in the presence of an external magnetic field B is carried out with the aim of achieving a high-precision magnetometer. We determine the uncertainty ΔB of such a device due to Gilbert dissipation and the associated internal magnetic field fluctuations that give rise to diffusion of the MN axis direction n and the needle orbital angular momentum. The levitation of the MN in a magnetic trap and its stability are also analyzed.

Insulating Josephson Junction Chains as Pinned Luttinger Liquids.

Quantum physics in one spatial dimension is remarkably rich, yet even with strong interactions and disorder, surprisingly tractable. This is due to the fact that the low-energy physics of nearly all one-dimensional systems can be cast in terms of the Luttinger liquid, a key concept that parallels that of the Fermi liquid in higher dimensions. Although there have been many theoretical proposals to use linear chains and ladders of Josephson junctions to create novel quantum phases and devices, only modest progress has been made experimentally. One major roadblock has been understanding the role of disorder in such systems. We present experimental results that establish the insulating state of linear chains of submicron Josephson junctions as Luttinger liquids pinned by random offset charges, providing a one-dimensional implementation of the Bose glass, strongly validating the quantum many-body theory of one-dimensional disordered systems. The ubiquity of such an electronic glass in Josephson-junction chains has important implications for their proposed use as a fundamental current standard, which is based on synchronization of coherent tunneling of flux quanta (quantum phase slips).

Geometric quantum noise of spin.

The presence of geometric phases is known to affect the dynamics of the systems involved. Here, we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nanomagnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application, we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.

Strong coupling of spin qubits to a transmission line resonator.

We propose a mechanism for coupling spin qubits formed in double quantum dots to a superconducting transmission line resonator. Coupling the resonator to the gate controlling the interdot tunneling creates a spin qubit-resonator interaction with a strength of tens of MHz. This mechanism allows operating the system at a symmetry point where decoherence due to charge noise is minimized. The transmission line can serve as the shuttle, allowing for fast two-qubit operations including the generation of qubit-qubit entanglement and the implementation of a controlled-phase gate.

Jordan-Wigner transformations for tree structures.

The celebrated Jordan-Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension. Here we extend this spin-fermion mapping to arbitrary tree structures, which enables mapping between fermionic and spin systems with nearest-neighbor coupling. The mapping is achieved with the help of additional spins at the junctions between one-dimensional chains. This property allows for straightforward simulation of Majorana braiding in spin or qubit systems.

Fingerprints of single nuclear spin energy levels using STM - ENDOR.

We performed STM-ENDOR experiments where the intensity of one of the hyperfine components detected in ESR-STM is recorded while an rf power is irradiated into the tunneling junction and its frequency is swept. When the latter frequency is near a nuclear transition a dip in ESR-STM signal is observed. This experiment was performed in three different systems: near surface SiC vacancies where the electron spin is coupled to a next nearest neighbor 29Si nucleus; Cu deposited on Si(111)7x7 surface, where the unpaired electron of the Cu atom is coupled to the Cu nucleus (63Cu, 65Cu) and on Tempo molecules adsorbed on Au(111), where the unpaired electron is coupled to a Nitrogen nucleus (14N). While some of the hyperfine values are unresolved in the ESR-STM data due to linewidth we find that they are accurately determined in the STM-ENDOR data including those from remote nuclei, which are not detected in the ESR-STM spectrum. Furthermore, STM-ENDOR can measure single nuclear Zeeman frequencies, distinguish between isotopes through their different nuclear magnetic moments and detect quadrupole spectra. We also develop and solve a Bloch type equation for the coupled electron-nuclear system that facilitates interpretation of the data. The improved spectral resolution of STM - ENDOR opens many possibilities for nanometric scale chemical analysis.

Decoherence spectroscopy with individual two-level tunneling defects.

Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.

Photon-number squeezing in circuit quantum electrodynamics.

A superconducting single-electron transistor (SSET) coupled to an anharmonic oscillator, e.g., a Josephson junction-L-C circuit, can drive the latter to a nonequilibrium photon-number distribution. By biasing the SSET at the Josephson quasiparticle cycle, cooling of the oscillator as well as a laserlike enhancement of the photon number can be achieved. Here, we show that the cutoff in the quasiparticle tunneling rate due to the superconducting gap, in combination with the anharmonicity of the oscillator, may create strongly squeezed photon-number distributions. For low dissipation in the oscillator, nearly pure Fock states can be produced.

Towards a dephasing diode: asymmetric and geometric dephasing.

We study the effect of a noisy environment on spin and charge transport in ballistic quantum wires with spin-orbit coupling (Rashba coupling). We find that the wire then acts as a dephasing diode, inducing very different dephasing of the spins of right and left movers. We also show how Berry phase (geometric phase) in a curved wire can induce such asymmetric dephasing, in addition to purely geometric dephasing. We propose ways to measure these effects through spin detectors, spin-echo techniques, and Aharanov-Bohm interferometry.

Single-qubit lasing and cooling at the Rabi frequency.

For a superconducting qubit driven to perform Rabi oscillations and coupled to a slow electromagnetic or nanomechanical oscillator we describe previously unexplored quantum optics effects. When the Rabi frequency is tuned to resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and a bistability with lasing behavior of the oscillator; for red detuning the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit-oscillator coupling is quadratic and decoherence effects are minimized. There the system realizes a "single-atom-two-photon laser."

Geometrical spin dephasing in quantum dots.

We study spin-orbit mediated relaxation and dephasing of electron spins in quantum dots. We show that higher order contributions provide a relaxation mechanism that dominates for low magnetic fields and is of geometrical origin. In the low-field limit relaxation is dominated by coupling to electron-hole excitations and possibly 1/f noise rather than phonons.

Geometric nature of the environment-induced Berry phase and geometric dephasing.

We investigate the geometric phase or Berry phase acquired by a spin half which is both subject to a slowly varying magnetic field and weakly coupled to a dissipative environment (either quantum or classical). We study how this phase is modified by the environment and find that the modification is of a geometric nature. While the original Berry phase (for an isolated system) is the flux of a monopole field through the loop traversed by the magnetic field, the environment-induced modification of the phase is the flux of a quadrupolelike field. We find that the environment-induced phase is complex, and its imaginary part is a geometric contribution to dephasing. Its sign depends on the direction of the loop. Unlike the Berry phase, this geometric dephasing is gauge invariant for open paths of the magnetic field.

Low- and high-frequency noise from coherent two-level systems.

Recent experiments indicate a connection between the low- and high-frequency noises affecting superconducting quantum systems. We explore the possibilities that both noises can be produced by one ensemble of microscopic modes, made up, e.g., by sufficiently coherent two-level systems (TLS's). This implies a relation between the noise power in different frequency domains, which depends on the distribution of the parameters of the TLS's. We show that a distribution, natural for tunneling TLS's, with a log-uniform distribution in the tunnel splitting and linear distribution in the bias, accounts for experimental observations.

Spin-spin correlators in the 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.

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.