Nanoscale magnetometry using a single spin system in diamond

We propose a protocol to estimate magnetic fields using a single nitrogen-vacancy (N-V) center in diamond, where the estimate precision scales inversely with time, ~1/T$, rather than the square-root of time. The method is based on converting the task of magnetometry into phase estimation, performing quantum phase estimation on a single N-V nuclear spin using either adaptive or nonadaptive feedback control, and the recently demonstrated capability to perform single-shot readout within the N-V [P. Neumann et. al., Science 329, 542 (2010)]. We present numerical simulations to show that our method provides an estimate whose precision scales close to ~1/T (T is the total estimation time), and moreover will give an unambiguous estimate of the static magnetic field experienced by the N-V. By combining this protocol with recent proposals for scanning magnetometry using an N-V, our protocol will provide a significant decrease in signal acquisition time while providing an unambiguous spatial map of the magnetic field.Comment: 8 pages and 5 figure

A simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling

We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Niels Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained because the scaling leaves invariant the position-momentum commutator. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential energy curves for the lowest singlet, triplet and excited states of H_2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Letter

Quantum Charged Spinning Particles in a Strong Magnetic Field (a Quantal Guiding Center Theory)

A quantal guiding center theory allowing to systematically study the separation of the different time scale behaviours of a quantum charged spinning particle moving in an external inhomogeneous magnetic filed is presented. A suitable set of operators adapting to the canonical structure of the problem and generalizing the kinematical momenta and guiding center operators of a particle coupled to a homogenous magnetic filed is constructed. The Pauli Hamiltonian rewrites in this way as a power series in the magnetic length $l_B= \sqrt{\hbar c/eB}$ making the problem amenable to a perturbative analysis. The first two terms of the series are explicitly constructed. The effective adiabatic dynamics turns to be in coupling with a gauge filed and a scalar potential. The mechanism producing such magnetic-induced geometric-magnetism is investigated in some detail.Comment: LaTeX (epsfig macros), 27 pages, 2 figures include

On Geometric Phase from Pure Projections

The geometric phase is usually treated as a quantity modulo 2\pi, a convention carried over from early work on the subject. The results of a series of optical interference experiments involving polarization of light, done by the present author (reviewed in R.Bhandari, Phys. Rep. 281 (1997) p.1) question the usefulness of such a definition of the geometric phase in that it throws away useful and measurable information about the system, for example strengths of singularities giving rise to the geometric phase. Such singularities have been directly demonstrated by phase-shift measurement in interference experiments. In this paper, two recent polarization experiments (Hariharan et.al., J.Mod.Opt. 44 (1997)p.707 and Berry and Klein, J.Mod.Opt. 43 (1996)p.165) are analysed and compared with previous experiments and potentially detectible singularities in these experiments pointed out.Comment: Latex, 15 pages, 6 figures; ([email protected]

Geometric phases and hidden local gauge symmetry

The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a sub-class of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases.Comment: 25 pages, 1 figure. Some typos have been corrected. To be published in Phys. Rev.

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

Quantum anomaly and geometric phase; their basic differences

It is sometimes stated in the literature that the quantum anomaly is regarded as an example of the geometric phase. Though there is some superficial similarity between these two notions, we here show that the differences bewteen these two notions are more profound and fundamental. As an explicit example, we analyze in detail a quantum mechanical model proposed by M. Stone, which is supposed to show the above connection. We show that the geometric term in the model, which is topologically trivial for any finite time interval $T$, corresponds to the so-called ``normal naive term'' in field theory and has nothing to do with the anomaly-induced Wess-Zumino term. In the fundamental level, the difference between the two notions is stated as follows: The topology of gauge fields leads to level crossing in the fermionic sector in the case of chiral anomaly and the {\em failure} of the adiabatic approximation is essential in the analysis, whereas the (potential) level crossing in the matter sector leads to the topology of the Berry phase only when the precise adiabatic approximation holds.Comment: 28 pages. The last sentence in Abstract has been changed, the last paragraph in Section 1 has been re-written, and the latter half of Discussion has been replaced by new materials. New Conclusion to summarize the analysis has been added. This new version is to be published in Phys. Rev.

Calculation of the Aharonov-Bohm wave function

A calculation of the Aharonov-Bohm wave function is presented. The result is a series of confluent hypergeometric functions which is finite at the forward direction.Comment: 12 pages in LaTeX, and 3 PostScript figure

Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?

Probably not.Comment: 10 pages, 1 figur