Quantum Kalman filtering and the Heisenberg limit in atomic magnetometry

The shot-noise detection limit in current high-precision magnetometry [Nature (London) 422, 596 (2003)] is a manifestation of quantum fluctuations that scale as 1/sqrt[N] in an ensemble of N atoms. Here, we develop a procedure that combines continuous measurement and quantum Kalman filtering [Rep. Math. Phys. 43, 405 (1999)]] to surpass this conventional limit by exploiting conditional spin squeezing to achieve 1/N field sensitivity. Our analysis demonstrates the importance of optimal estimation for high bandwidth precision magnetometry at the Heisenberg limit and also identifies an approximate estimator based on linear regression.     

Can a quantum nondemolition measurement improve the sensitivity of an atomic magnetometer?

We consider the limitations due to noise (e.g., quantum projection noise and photon shot-noise) on the sensitivity of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of N atomic spins by detecting optical rotation of far-detuned light. We show that for very short measurement times, the optimal sensitivity scales as N(-3/4); if strongly squeezed probe light is used, the Heisenberg limit of N-1 scaling can be achieved. However, if the measurement time exceeds tau(rel)/N(1/2) in the former case, or tau(rel)/N in the latter, where tau(rel) is the spin relaxation time, the scaling becomes N(-1/2), as for a standard shot-noise-limited magnetometer.     

Percolation transitions are not always sharpened by making networks interdependent

We study a model for coupled networks introduced recently by Buldyrev et al., [Nature (London) 464, 1025 (2010)], where each node has to be connected to others via two types of links to be viable. Removing a critical fraction of nodes leads to a percolation transition that has been claimed to be more abrupt than that for uncoupled networks. Indeed, it was found to be discontinuous in all cases studied. Using an efficient new algorithm we verify that the transition is discontinuous for coupled Erd?s-Rényi networks, but find it to be continuous for fully interdependent diluted lattices. In 2 and 3 dimensions, the order parameter exponent β is larger than in ordinary percolation, showing that the transition is less sharp, i.e., further from discontinuity, than for isolated networks. Possible consequences for spatially embedded networks are discussed.     

How irrelevant operators affect the determination of fractional charge

We show that the inclusion of irrelevant terms in the Hamiltonian describing tunneling between edge states in the fractional quantum Hall effect can lead to a variety of nonperturbative behaviors in intermediate energy regimes and, in particular, affect crucially the determination of charge through shot noise measurements. We show, for instance, that certain combinations of relevant and irrelevant terms can lead to an effective measured charge nue in the strong backscattering limit and an effective measured charge e in the weak backscattering limit, in sharp contrast with standard perturbative expectations. This provides a possible scenario to explain the experimental observations by Comforti et al. [Nature (London) 416, 515 (2002)]], which are so far not understood.     

Strongly enhanced spin squeezing via quantum control

We describe a new approach to spin squeezing based on a double-pass Faraday interaction between an optical probe and an optically dense atomic sample. A quantum eraser is used to remove residual spin-probe entanglement, thereby realizing a single-axis twisting unitary map on the collective spin. This interaction can be phase matched, resulting in exponential enhancement of squeezing as a function of optical density for times short compared to the decoherence time. In practice the scaling and peak squeezing depends on decoherence, technical loss, and noise. Including these imperfections, our model indicates that ～10 dB of squeezing should be achievable with laboratory parameters.     

Geometric frustration and dimensional reduction at a quantum critical point

We show that the spatial dimensionality of the quantum critical point associated with Bose-Einstein condensation at T=0 is reduced when the underlying lattice comprises layers coupled by a frustrating interaction. Our theoretical predictions for the critical behavior correspond very well with recent measurements in BaCuSi(2)O(6) [ S. E. Sebastian et al., Nature (London) 441, 617 (2006)].     

Nuclear structure corrections in muonic deuterium

The muonic hydrogen experiment measuring the 2P-2S transition energy [R. Pohl et?al., Nature (London) 466, 213 (2010)] is significantly discrepant with theoretical predictions based on quantum electrodynamics. A possible approach to resolve this conundrum is to compare experimental values with theoretical predictions in another system, muonic deuterium μD. The only correction which might be questioned in μD is that due to the deuteron polarizability. We investigate this effect in detail and observe cancellation with the elastic contribution. The total value obtained for the deuteron structure correction in the 2P-2S transition is 1.680(16)?meV.     

Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement

We demonstrate spin squeezing in a room temperature ensemble of approximately 10(12) cesium atoms using their internal structure, where the necessary entanglement is created between nuclear and electronic spins of each individual atom. This state provides improvement in measurement sensitivity beyond the standard quantum limit for quantum memory experiments and applications in quantum metrology and is thus a complementary alternative to spin squeezing obtained via interatom entanglement. Squeezing of the collective spin is verified by quantum state tomography.     

Quantum coherence in the time-resolved Auger measurement

We present a quantum mechanical model of the attosecond-XUV (extreme ultraviolet) pump and laser probe measurement of an Auger decay [Drescher et al., Nature (London) 419, 803 (2002)]] and investigate effects of quantum coherence. The time-dependent Schr?dinger equation is solved by numerical integration and in analytic form. We explain the transition from a quasiclassical energy shift of the spectrum to the formation of sidebands and the enhancement of high- and low-energy tails of the Auger spectrum due to quantum coherence between photoionization and Auger decay.     

Quantum Fisher information and spin squeezing in one-axis twisting model

We investigate the dependence of the average parameter estimation precision （APEP）, which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state ｜θ0,φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 （2009） 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near- Heisenberg limit 2IN in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0- π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEE     

Quantum entanglement formation by repeated spin blockade measurements in a spin field-effect transistor structure embedded with quantum dots

We propose a method of operating a quantum state machine made of stacked quantum dots buried in adjacent to the channel of a spin field-effect transistor (FET) [S. Datta, B. Das, Appl. Phys. Lett. 56 (1990) 665; K. Yoh, et al., Proceedings of the 23rd International Conference on Physics of Semiconductors (ICPS) 2004; H. Ohno, K. Yoh et al., Jpn. J. Appl. Phys. 42 (2003) L87; K. Yoh, J. Konda, S. Shiina, N. Nishiguchi, Jpn. J. Appl. Phys. 36 (1997) 4134]. In this method, a spin blockade measurement extracts the quantum state of a nearest quantum dot through Coulomb blockade [K. Yoh, J. Konda, S. Shiina, N. Nishiguchi, Jpn. J. Appl. Phys. 36 (1997) 4134; K. Yoh, H. Kazama, Physica E 7 (2000) 440] of the adjacent channel conductance. Repeated quantum Zeno-like (QZ) measurements [H. Nakazato, et al., Phys. Rev. Lett. 90 (2003) 060401] of the spin blockade is shown to purify the quantum dot states within several repetitions. The growth constraints of the stacked InAs quantum dots are shown to provide an exchange interaction energy in the range of 0.01–1 meV [S. Itoh, et al., Jpn. J. Appl. Phys. 38 (1999) L917; A. Tackeuchi, et al., Jpn. J. Appl. Phys. 42 (2003) 4278]. We have verified that one can reach the fidelity of 90% by repeating the measurement twice, and that of 99.9% by repeating only eleven QZ measurements. Entangled states with two and three vertically stacked dots are achieved with the sampling frequency of the order of 100 MHz.     

Sub-shot-noise magnetometry with a correlated spin-relaxation dominated alkali-metal vapor

Spin noise sets fundamental limits to the precision of measurements using spin-polarized atomic vapors, such as performed with sensitive atomic magnetometers. Spin squeezing offers the possibility to extend the measurement precision beyond the standard quantum limit of uncorrelated atoms. Contrary to current understanding, we show that, even in the presence of spin relaxation, spin squeezing can lead to a significant reduction of spin noise, and hence an increase in magnetometric sensitivity, for a long measurement time. This is the case when correlated spin relaxation due to binary alkali-atom collisions dominates independently acting decoherence processes, a situation realized in thermal high atom-density magnetometers and clocks.     

Quantum critical Kondo quasiparticles probed by ESR in β-YbAlB₄

Electron spin resonance (ESR) can probe conduction electrons (CE) and local moment (LM) spin systems in different materials. A CE spin resonance (CESR) is observed in metallic systems based on light elements or with enhanced Pauli susceptibility. LM ESR can be seen in compounds with paramagnetic ions and localized d or f electrons. Here we report a remarkable and unprecedented ESR signal in the heavy-fermion superconductor β-YbAlB? [S. Nakatsuji et al., Nature Phys. 4, 603 (2008)] which behaves as a CESR at high temperatures and acquires characteristics of the Yb3? LM ESR at low temperature. This dual behavior strikes as an in situ unique observation of the Kondo quasiparticles in a quantum critical regime. The proximity to a quantum critical point may favor the appearance of this dual character of the ESR signal in β-YbAlB?.     

Spin ice: magnetic excitations without monopole signatures using muon spin rotation

Theory predicts the low temperature magnetic excitations in spin ices consist of deconfined magnetic charges, or monopoles. A recent transverse-field (TF) muon spin rotation (μSR) experiment [S.?T. Bramwell et al., Nature (London) 461, 956 (2009)] reports results claiming to be consistent with the temperature and magnetic field dependence anticipated for monopole nucleation-the so-called second Wien effect. We demonstrate via a new series of μSR experiments in Dy(2)Ti(2)O(7) that such an effect is not observable in a TF μSR experiment. Rather, as found in many highly frustrated magnetic materials, we observe spin fluctuations which become temperature independent at low temperatures, behavior which dominates over any possible signature of thermally nucleated monopole excitations.     

Procedure for direct measurement of general quantum states using weak measurement

Recent work by Lundeen et al. [Nature (London) 474, 188 (2011)] directly measured the wave function by weakly measuring a variable followed by a normal (i.e., "strong") measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of various products of these observables, thereby providing the density matrix an operational definition in terms of a procedure for its direct measurement. The method only requires measurements in two bases and can be performed in situ, determining the quantum state without destroying it.     

Propagation of spin information at the supramolecular scale through heteroaromatic linkers

We report an in-depth study on how spin information propagates at supramolecular scale through a family of heteroaromatic linkers. By density-functional theory calculations, we rationalize the behavior of a series of Cr7Ni dimers for which we are able to systematically change the aromatic linker thus tuning the strength of the magnetic interaction, as experimentally shown by low temperature micro-SQUID and specific heat measurements. We also predict a cos2 dependence of the magnetic coupling on the twisting angle between the aromatic cycles in bicyclic linkers, a mechanism parallel to charge transport on similar systems [L. Venkataraman et al., Nature (London) 442, 904 (2006)].     

Emergence of atypical properties in assembled graphene nanoribbons

Graphitic nanowiggles (GNWs) are periodic repetitions of nonaligned finite-sized graphitic nanoribbon domains seamlessly stitched together without structural defects. These complex nanostructures have been recently fabricated [Cai et al., Nature (London) 466, 470 (2010)] and are here predicted to possess unusual properties, such as tunable band gaps and versatile magnetic behaviors. We used first-principles theory to highlight the microscopic origins of the emerging electronic and magnetic properties of the main subclasses of GNWs. Our study establishes a road map for guiding the design and synthesis of specific GNWs for nanoelectronic, optoelectronic, and spintronic applications.     

Impossibility of the counterfactual computation for all possible outcomes

A recent proposal for counterfactual computation [O. Hosten et al. Nature (London) 439, 949 (2006) is analyzed. It is argued that the method does not provide counterfactual computation for all possible outcomes. The explanation involves a novel paradoxical feature of pre- and postselected quantum particles: The particle can reach a certain location without being on the path that leads to this location.     

Simultaneous Space and Time Synchronization Using Shared Entangled Qubits

This paper generalizes the quantum clock synchronization protocol of Josza, et al., [Richard Jozsa, et al.,Phys. Rev. Lett. 85 (2000) 2010] to synchronize space and thne simultaneously.