Single-Atom Gating of Quantum State Superpositions

The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric interpretation: this state space--or Hilbert space--is spanned by mutually orthogonal state vectors corresponding to the quantized degrees of freedom of the real-space system. Measurement of superpositions is akin to accessing the direction of a vector in Hilbert space, determining an angle of rotation equivalent to quantum phase. Here we show that an individual atom inside a designed quantum corral can control this angle, producing arbitrary coherent superpositions of spatial quantum states. Using scanning tunnelling microscopy and nanostructures assembled atom-by-atom we demonstrate how single spins and quantum mirages can be harnessed to image the superposition of two electronic states. We also present a straightforward method to determine the atom path enacting phase rotations between any desired state vectors. A single atom thus becomes a real space handle for an abstract Hilbert space, providing a simple technique for coherent quantum state manipulation at the spatial limit of condensed matter.Comment: Published online 6 April 2008 in Nature Physics; 17 page manuscript (including 4 figures) + 3 page supplement (including 2 figures); supplementary movies available at http://mota.stanford.ed

Beyond Logarithmic Corrections to Cardy Formula

As shown by Cardy modular invariance of the partition function of a given unitary non-singular 2d CFT with left and right central charges c_L and c_R, implies that the density of states in a microcanonical ensemble, at excitations Delta and Delta-bar and in the saddle point approximation, is \rho_0(\Delta,\bar\Delta;c_L, c_R)=c_L c_R \exp(2\pi\sqrt{{c_L\Delta}/{6}})\exp(2\pi\sqrt{{c_R\bar\Delta}/{6}}). In this paper, we extend Cardy's analysis and show that in the saddle point approximation and up to contributions which are exponentially suppressed compared to the leading Cardy's result, the density of states takes the form \rho(\Delta,\bar\Delta; c_L,c_R)= f(c_L\Delta) f(c_R\bar\Delta)\rho_0(\Delta,\bar\Delta; c_L, c_R), for a function f(x) which we specify. In particular, we show that (i) \rho (\Delta,\bar\Delta; c_L, c_R) is the product of contributions of left and right movers and hence, to this approximation, the partition function of any modular invariant, non-singular unitary 2d CFT is holomorphically factorizable and (ii) \rho(\Delta,\bar\Delta; c_L, c_R)/(c_Lc_R) is only a function of $c_R\bar\Delta$ and $c_L\Delta$. In addition, treating \rho(\Delta,\bar\Delta; c_L, c_R) as the density of states of a microcanonical ensemble, we compute the entropy of the system in the canonical counterpart and show that the function f(x) is such that the canonical entropy, up to exponentially suppressed contributions, is simply given by the Cardy's result \ln\rho_0(\Delta,\bar\Delta; c_L, c_R).Comment: 30 pages, no figures; v2: minor improvements, one reference added, v3: minor corrections to match the published versio

Domain wall brane in squared curvature gravity

We suggest a thick braneworld model in the squared curvature gravity theory. Despite the appearance of higher order derivatives, the localization of gravity and various bulk matter fields is shown to be possible. The existence of the normalizable gravitational zero mode indicates that our four-dimensional gravity is reproduced. In order to localize the chiral fermions on the brane, two types of coupling between the fermions and the brane forming scalar is introduced. The first coupling leads us to a Schr\"odinger equation with a volcano potential, and the other a P\"oschl-Teller potential. In both cases, the zero mode exists only for the left-hand fermions. Several massive KK states of the fermions can be trapped on the brane, either as resonant states or as bound states.Comment: 18 pages, 5 figures and 1 table, references added, improved version to be published in JHE

Effort-related functions of nucleus accumbens dopamine and associated forebrain circuits

Background Over the last several years, it has become apparent that there are critical problems with the hypothesis that brain dopamine (DA) systems, particularly in the nucleus accumbens, directly mediate the rewarding or primary motivational characteristics of natural stimuli such as food. Hypotheses related to DA function are undergoing a substantial restructuring, such that the classic emphasis on hedonia and primary reward is giving way to diverse lines of research that focus on aspects of instrumental learning, reward prediction, incentive motivation, and behavioral activation. Objective The present review discusses dopaminergic involvement in behavioral activation and, in particular, emphasizes the effort-related functions of nucleus accumbens DA and associated forebrain circuitry. Results The effects of accumbens DA depletions on food-seeking behavior are critically dependent upon the work requirements of the task. Lever pressing schedules that have minimal work requirements are largely unaffected by accumbens DA depletions, whereas reinforcement schedules that have high work (e.g., ratio) requirements are substantially impaired by accumbens DA depletions. Moreover, interference with accumbens DA transmission exerts a powerful influence over effort-related decision making. Rats with accumbens DA depletions reallocate their instrumental behavior away from food-reinforced tasks that have high response requirements, and instead, these rats select a less-effortful type of food-seeking behavior. Conclusions Along with prefrontal cortex and the amygdala, nucleus accumbens is a component of the brain circuitry regulating effort-related functions. Studies of the brain systems regulating effort-based processes may have implications for understanding drug abuse, as well as energy-related disorders such as psychomotor slowing, fatigue, or anergia in depression

Worth the ‘EEfRT’? The Effort Expenditure for Rewards Task as an Objective Measure of Motivation and Anhedonia

Background: Of the putative psychopathological endophenotypes in major depressive disorder (MDD), the anhedonic subtype is particularly well supported. Anhedonia is generally assumed to reflect aberrant motivation and reward responsivity. However, research has been limited by a lack of objective measures of reward motivation. We present the Effort-Expenditure for Rewards Task (EEfRT or ‘‘effort’’), a novel behavioral paradigm as a means of exploring effort-based decision-making in humans. Using the EEfRT, we test the hypothesis that effort-based decision-making is related to trait anhedonia. Methods/Results: 61 undergraduate students participated in the experiment. Subjects completed self-report measures of mood and trait anhedonia, and completed the EEfRT. Across multiple analyses, we found a significant inverse relationship between anhedonia and willingness to expend effort for rewards. Conclusions: These findings suggest that anhedonia is specifically associated with decreased motivation for rewards, and provide initial validation for the EEfRT as a laboratory-based behavioral measure of reward motivation and effort-base