We present experimental proof that in rotating 3 He-Z? the vortex-core transition temperature 7V separates axisymmetric vortices above TV from vortices with spontaneously broken axial symmetry below TV. The nonaxisymmetry is observed in the presence of coherent spin precession as a new soft Goldstone mode, manifested as oscillations and spiral twisting of the core anisotropy axis. These are driven by the precessing spin via spin-orbit coupling and lead to magnetic relaxation from viscous losses, which depend on vortex pinning.PACS numbers: 67.50.FiThe quantized vortices of superfluid He-Z? were discovered in 1981: An abrupt change in NMR frequency shifts at a critical phase-transition line Ty(p) in the temperature-(T-) pressure (p) plane was interpreted to represent a change in the structure of the vortex core. l Theoretical investigations 2,3 in the Ginzburg-Landau regime close to T c revealed two types of vortices with the same number of circulation quanta but with different internal symmetries of their cores. At high pressure the most stable vortex is the axisymmetric V\ vortex 2 with broken parity and with 3 He-A superfluid inside a core with a diameter of several coherence lengths £o~13 nm. At low pressure the rotational symmetry is broken, resulting in the V2 vortex with a nonaxisymmetric double core, 3 which may be considered a bound state of two half-quantum vortices (see insets in Fig. 1). This is now regarded as being consistent with existing experimental information. 4 Here we present the first direct experimental evidence that the phase transition, indeed, separates an axisymmetric V\ vortex at high temperatures from an asymmetric V2 vortex at low temperatures. The results were obtained by making use of the homogeneously precessing magnetic domain 5 (HPD), an NMR mode of 3 He-Z? which has proven to be more sensitive to the core structure than conventional NMR. In the HPD mode all spins within the resonance domain precess uniformly at a tipping angle of roughly 104°. Several relaxation mechanisms contribute to losses in this mode; however, here we are only concerned with the absorption caused by vortices. 6 This additional absorption Py is proportional to the total length of vortices within the precessing domain and increases discontinuously by a factor of 3 at Tyip) during cooling. 7 It also turns out that the HPD absorption of a vortex array with a constant number Ny of V2 vortices depends on whether or not the rotation velocity ft is maintained constant: If ft changes with time then an increase APf in the absorption level Pvi is observed. We explain this unique feature in terms of the dipolar coupling between the homogeneously precessing total spin magnetization and the orbital inhomogeneity in the vortex-core region. The HPD absorption from V2 vortices is dominated by a soft Goldstone mode, associated with the viscous dynamics of the in-plane orbital anisotropy vector b of the asymmetric vortex core. The Goldstone mode is manifested by (i) rapid viscous oscillatory motion and by (ii) slow rotationa...

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In NMR experiments and quantum computation, many pulse (quantum gate) sequences called the composite pulses, were developed to suppress one of two dominant errors; a pulse length error and an off-resonance error. We describe, in this paper, a general prescription to design a single-qubit concatenated composite pulse (CCCP) that is robust against two types of errors simultaneously. To this end, we introduce a new property, which is satisfied by some composite pulses and is sufficient to obtain a CCCP. Then we introduce a general method to design CCCPs with shorter execution time and less number of pulses. DRAFT taneously, although they are restricted within null operation and π-rotation (NOT gate) of a nuclear spin. In order to realize a composite pulse which is robust against these two errors simultaneously and without any restriction, we designed a ConCatenated Composite Pulse (CCCP) by concatenating CORPSE and SCROFULOUS. 16) The CCCP reported previously 16) consists of 3 composite pulses, each of which consists of 3 elementary pulses. Consequently, this CCCP is made of 9 pulses in total. Although this CCCP is robust against both PLE and ORE, its execution time is considerably longer than the corresponding elementary pulse. CCCPs made of less number of elementary pulses are certainly desirable from a viewpoint of decoherence suppression.Establishing general prescription to design a CCCP and its improvement are the subjects of this paper. Some composite pulses have interesting property, which we call the residualerror-preserving (REP) property. Employing two types of composite pulses with mutually exclusive REP properties is essential to design a successful CCCP robust against both PLE and ORE. By using this method, we obtain many CCCPs systematically. Moreover, we further

Nucleation of vortices in units of one quantum has been observed with C.W. NMR in a rotating cylinder filled with 3He-B. During acceleration a new vortex is created each time the counterflow velocity at the perimeter reaches a critical value v,(T, p ) . The measured v, resembles the calculated velocity v,b (T, p ) of the bulk superflow instability, but is smaller by a factor with power law dependence on the superfluid coherence length. This indicates that a nucleation event takes place whenever the flow exceeds v,b locally at the nucleation site and the nucleation barrier vanishes.

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We show that some composite pulses widely employed in nuclear magnetic resonance experiments are regarded as non-adiabatic geometric quantum gates with Aharanov-Anandan phases. Thus, we reveal the presence of a fundamental issue on quantum mechanics behind a traditional technique. To examine the robustness of such composite pulses against fluctuations, we present a simple noise model in a two-level system. Then, we find that the composite pulses possesses purely geometrical nature even under a certain type of fluctuations.PACS numbers: 03.65. Vf, 82.56.Jn, Geometric phases have been attracting a lot of attention from the view point of the foundation of quantum mechanics and mathematical physics [1,2,3,4]. Recently, their application to quantum information processing is spotlighted [5,6], because they are expected to be robust against noise. However, the robustness of a geometric quantum gate (GQG), which is a quantum gate only using geometric phases, is not completely verified. Various examinations on this issue have been reported [7,8,9,10,11,12]. Blais and Tremblay [7] claimed that no advantage of the GQGs exists compared to the corresponding quantum gates with dynamical phases, while Zhu and Zanardi [8] showed that their non-adiabatic GQGs are robust against fluctuations in control parameters.In this paper, we show that some composite pulses widely employed in nuclear magnetic resonance (NMR) [13,14] to accomplish reliable operations is regarded as non-adiabatic GQGs based on an Aharonov-Anandan (AA) phase [15], and propose a simple noise model in a two-level system. Then, we classify fluctuations in terms of the robustness of the GQGs.An AA phase appears under non-adiabatic cyclic time evolution of a quantum system [15]. We note that the generalization to the non-cyclic case is given in Ref. [3,16]. Let us write the Bloch vector at t (0 ≤ t ≤ 1) as n(t)(∈ R 3 ). We denote a state vector given n(t) as |n(t) (∈ C 2 ). Namely, n(t) = n(t)|σ|n(t) , where σ = t (σ x , σ y , σ z ). The symbol t means the transposition of a vector. Time evolution is described by the Schrödinger equation with the Hamiltonian H(t). Note that |n(t)| = 1. Hereafter, we denote n(0) as n. We take the natural unit system in which = 1. Suppose that |n(1) = e iγ |n (γ ∈ R): n(1) = n. The AA phase γ g is defined as [15] γ g = γ − γ d ,(1) * Present address: CCSE, Japan Atomic Energy Agency, 6-9-3 Higashi-Ueno, Tokyo 110-0015, Japan and CREST(JST), 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan where( 2) is a dynamical phase. Next, suppose n + and n − are two Bloch vectors satisfying (a) n + · n − = −1 (i.e., n + |n − = 0) and (b) n ± (1) = n ± (i.e., there exist γ ± ∈ R such that |n ± (1) = e iγ± |n ± . An arbitrary quantum state |n is expressed by |n = a + |n + + a − |n − , where a ± = n ± |n . We call n ± basis Bloch vector corresponding to H(t). The initial state |n is transformed into the final state |n(1) = a + e iγ+ |n + + a − e iγ− |n − . Thus, the time evolution operator U at t = 1 generated by H(t) (t ∈ [0, 1]) is rewritten as U =...

Hydrogen in porous Vycor glass ͑pore radius R p ϭ3.0 nm͒ has been investigated with a torsional oscillator technique at 7.5 K рTр 22 K. H 2 molecules which are adsorbed in Vycor at TϾT 3 (T 3 , triple point of bulk H 2 ) leave the Vycor when decreasing the temperature to below a characteristic value T c рT 3 ; T c depends on the amount of H 2 in the Vycor. This interpretation of the data is supported by simultaneous measurements of the H 2 vapor pressure. A similar phenomenon is observed with a capacitor filled with Vycor into which H 2 is condensed. We conclude that the free energy of solid H 2 in the Vycor is larger than that of bulk solid H 2 . Information on the free energy of H 2 confined in the Vycor is important to understand the depression of its freezing temperature in restricted geometries. We also discuss the properties of solids and the depression of their freezing temperature in restricted geometries.

We propose a simple formalism to design unitary gates robust against given systematic errors. This formalism generalizes our previous observation [Y. Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing dynamical phase in some composite gates is essential to suppress pulse-length errors. By employing our formalism, we derive a new composite unitary gate which can be seen as a concatenation of two known composite unitary operations. The obtained unitary gate has high fidelity over a wider range of error strengths compared to existing composite gates.