We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wave packet of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during our scheme. We find a remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling), and also a dynamical decoupling nature of the scheme itself. Together they secure a high visibility of the resulting Ramsey fringes. The mass independence of our scheme makes it viable for a nano-object selected from an ensemble with a high mass variability. Given these advantages, a quantum superposition with a 100 nm spatial separation for a massive object of 10^{9}  amu is achievable experimentally, providing a route to test postulated modifications of quantum theory such as continuous spontaneous localization.

We report the behavior of the electrochemical capacitance for a variety of atomic junctions using ab initio methods. The capacitance can be classified according to the nature of conductance and shows a remarkable crossover from a quantum dominated regime to that of a classical-like geometric behavior. Clear anomalies arise due to a finite density of states of the atomic junction as well as the role played by the atomic valence orbitals. The results suggest several experiments to study contributions due to quantum effects and the atomic degree of freedom. [S0031-9007(98)06031-1] PACS numbers: 73.40.Cg, 61.16.Ch, 61.43.BnFor a very small conductor in which quantum effects play a role, it is not difficult to imagine that capacitance of the conductor may behave differently from the familiar classical case. For a small conductor its discrete nature of electron energy levels can be important, and the quantum correction due to the finite density of states (DOS) of the plates is known as the quantum capacitance [1,2]. For a microscopic sized conductor in which quantum coherence is maintained, one must consider the role played by the leads which connect the conductor to the outside world. One also needs to consider the finite screening length of the interacting electrons when it is not small compared with the system size. At these very small length scales, the relevant capacitance is the electrochemical capacitance C ϵ edQ͞dm, which is a quantity depending on the electronic properties of the conductor [2].Capacitance plays a central role in many phenomena such as the Coulomb blockade, and it is very important for several experimental techniques. However, there have been no quantitative predictions of capacitance for microscopic systems. Thus, we do not yet know its dependence on the atomic valence orbitals, the environment (e.g., the leads), and the shape, size, and other properties of a nanosystem. The purpose of this work is to make this connection by theoretically investigating capacitance of atomic junctions. In particular we shall study junctions formed by a small cluster of atoms, shown in the right panel of Fig. 1, where the clusters are sandwiched in between two metallic leads. We emphasize small system size where quantum effects are dominant and we answer a number of very relevant questions: (i) What is the value of the capacitance of these atomic junctions? (ii) What is the effect of atomic orbitals? (iii) How do we characterize the behavior of the capacitance? (iv) For the tip-substrate system familiar to scanning tunneling microscopy (STM), what is the C C͑d͒? Although atomic nanosystems are of great current interest [3], these fundamental questions, which are important to ac transport, have not been addressed. It is clear that capacitance and many other mechanical and electrical properties of atomic junctions can be obtained only from detailed first principle analysis [4]. This will be our approach.The theoretical analysis consists of four steps. First, we determine the atomic cluster shape by extensive quant...

The static and dynamic response associated with a low concentration, x, of static defects in a Heisenberg antiferromagnet at zero temperature is analyzed within linearized spin-wave theory. We obtain the dispersion relation for long-wavelength spin waves in the form ω(q)= c (x) q + iγ(x) q τ. Our results for c(x) agree with previous work, and in particular give c(x) = c(0)[1 + αx + O(x 2)] where the coefficient α, which can be related to the helicity modulus and the uniform perpendicular susceptibility, diverges in the limit d→2, where d is the spatial dimensionality. One major new result is that τ=d−1 for defects whose spin, S', is different from that (S) of the host lattice and τ=d+1 when S'=S.

We have investigated quantum transport through long wires in which a section consists of one or several Al atoms in a chain. The self-consistent ground state electronic potential is obtained using the first principles ab initio method and the conductance is calculated by solving a three-dimensional quantum scattering problem. We have observed quantized conductance when there are two or more Al atoms in the chain. Resistance is calculated for these wires at the Fermi level.

Our papers [1,2] propose an experiment in which the observation of Ramsey fringes would be evidence for a spatial superposition. We analyzed this as a magnetic effect creating a Stern-Gerlach like spin dependent separation of the centre of mass (COM) states in conjunction with a gravitational effect imparting a relative phase between the states. The comment points out that this could be interpreted in a different way. It contends that the interference manifested in the spin states is not due to the spatial separation as the gravity effects can also be interpreted as a Zeeman effect. To support its contention, the comment splits the Hamitonian into parts H 1 and H 2 where only H 1 couples the COM with the spin states, while H 2 imparts the phase factor. However, the periodic factorizability of the COM and the spin states requires the action of H 1 as well. It is this factorizability which makes the phase detectable by a measurement on the spin alone. For instance, if the COM and spin states are not entangled at T /2, the evolution by H 1 alone for an additional time T /2 will not be able to factorise them. This will lead to the Ramsey interference pattern being supressed. Thus the very visibility of the phase due to H 2 hinges on the interference brought about by H 1 . Both treatments (our's and the comment's) are valid and equivalent as they use the same Hamiltonian. In both cases there is a spatial superposition except for certain periodic moments in time (at integer multiples of the oscillator time period T ). In both cases, the absence of coherence in the COM motion (which could be due to decoherence from air molecules for example) would remove these fringes.In the absence of decoherence, an arbitrary initial coherent state |β of the COM and an initial spin statewhere |β(t, ±1) are COM coherent states with the timevarying separation of ∆z(t) = 8λδz ωz (1 − cos ω z t) with δ z = 2mωz being the ground state position spread of the oscillator. Despite the fact that |β(t, ±1) oscillate about centresωz where there are finite magnetic fields, in our approach, the entire inhomogeneous magnetic field term of the Hamitonian is "used up" to accompish the Stern-Gerlach like separation ∆z(t), and is thereby, not available any more to impart a Zeeman phase between the separated states. The integrated gravitational phase shift T 0 mg cos θ∆z(t)dt gives exactly theLet us now clarify that even if the comment's interpretation that the measured signal results from "the common displacement of the COM position of both ±1 states" is adopted, the visibility of this signal is affected by the coherence between the superposed COM states. Consider a case where only the COM motion is decohered: the off diagonal terms |β(t, +1) β(t, −1)| are damped by a factor of e −γ(t) . Then the evolved state at t = N T isThus we see that the spin density matrix has also decohered (thereby lowering the visibility of φ as a relevant parameter, say θ, is varied) despite the fact that the decoherence was exclusively for the COM state [3,4]. In particular...