We consider theoretically the novel technique in magnetic resonance force microscopy which is called ``oscillating cantilever-driven adiabatic reversals''. We present analytical and numerical analysis for the stationary cantilever vibrations in this technique. For reasonable values of parameters we estimate the resonant frequency shift as 6Hz per the Bohr magneton. We analyze also the regime of small oscillations of the paramagnetic moment near the transversal plane and the frequency shift of the damped cantilever vibrations.
We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We estimated the frequency shift of the cantilever vibrations and demonstrated that this shift causes the formation of a Schrodinger cat state which has some similarities and differences from the conventional MRFM technique which uses cyclic adiabatic reversals of spins. The interaction of the cantilever with the environment is shown to quickly destroy the coherence between the two possible cantilever trajectories. We have shown that using…
Magnetic Resonance Force Microscopy (MRFM) is an emergent technology for measuring spin-induced attonewton forces using a micromachined cantilever. In the interrupted Oscillating Cantilever-driven Adiabatic Reversal (iOSCAR) method, small ensembles of electron spins are manipulated by an external radio frequency (RF) magnetic field to produce small periodic deviations in the resonant frequency of the cantilever. These deviations can be detected by frequency demodulation, followed by conventional amplitude or energy detection. In this paper, we develop optimal detectors for several signal model…
We consider the process of spin relaxation in the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. We simulated the spin relaxation caused by thermal excitations of the high frequency cantilever modes in the region of the Rabi frequency of the spin sub-system. The minimum relaxation time obtained in our simulations is greater but of the same order of magnitude as one measured in recent experiments. We demonstrated that using a cantilever with nonuniform cross-sectional area may significantly increase spin relaxation time.
We simulate magnetic resonance force microscopy measurements of an entangled spin state. One of the entangled spins drives the resonant cantilever vibrations, while the other remote spin does not interact directly with the quasiclassical cantilever. The Schrödinger cat state of the cantilever reveals two possible outcomes of the measurement for both entangled spins.
We study the quantum dynamics of a model for the single-spin measurement in magnetic-resonance force microscopy. We consider an oscillating driven cantilever coupled with the magnetic moment of the sample. Then, the cantilever is damped through an external bath and its readout is provided by a radiation field. Conditions for reliable measurements will be discussed.
We determine the quantum mechanical limits to inertial mass-sensing based on nanomechanical systems. We first consider a harmonically oscillating cantilever whose vibration frequency is changed by mass accretion at its surface. We show that its zero-point fluctuations limit the mass sensitivity, for attainable parameters, to about an electron mass. In contrast to the case of a classical cantilever, we find the mass sensitivity of the quantum mechanical cantilever is independent of its resonant frequency in a certain parameter regime at low temperatures. We then consider an optomechanical setup…
Magnetic resonance in an ensemble of laser-cooled trapped Rb atoms is excited using a micro- cantilever with a magnetic tip. The cantilever is mounted on a multi-layer chip designed to capture, cool, and magnetically transport cold atoms. The coupling is observed by measuring the loss from a magnetic trap as the oscillating cantilever induces Zeeman state transitions in the atoms. Interfacing cold atoms with mechanical devices could enable probing and manipulating atomic spins with nanometer spatial resolution and single-spin sensitivity, leading to new capabilities in quantum computation, qua…
We study the effects of wave function collapses in the oscillating cantilever driven adiabatic reversals (OSCAR) magnetic resonance force microscopy (MRFM) technique. The quantum dynamics of the cantilever tip (CT) and the spin is analyzed and simulated taking into account the magnetic noise on the spin. The deviation of the spin from the direction of the effective magnetic field causes a measurable shift of the frequency of the CT oscillations. We show that the experimental study of this shift can reveal the information about the average time interval between the consecutive collapses of the …
A promising technique for measuring single electron spins is magnetic resonance force microscopy (MRFM), in which a microcantilever with a permanent magnetic tip is resonantly driven by a single oscillating spin. If the quality factor of the cantilever is high enough, this signal will be amplified over time to the point that it can be detected by optical or other techniques. An important requirement, however, is that this measurement process occur on a time scale short compared to any noise which disturbs the orientation of the measured spin. We describe a model of spin noise for the MRFM syst…
We developed a discrete two-dimensional model of a cantilever which incorporates the effects of inhomogeneity, the geometry of an attached particle, and the influence of external time-dependent forces. We provide a comparison between the solutions for our discrete model and its continuous limit. The rotational-vibrational mode is studied in detail. The results of numerical simulations demonstrate usefulness of our model for many applications when a cantilever has a complicated geometry and is affected by time-depended and distributed external forces.
The efficient cooling of the nanomechanical resonators is essential to exploration of quantum properties of the macroscopic or mesoscopic systems. We propose such a laser-cooling scheme for a nanomechanical cantilever, which works even for the low-frequency mechanical mode and under weak cooling lasers. The cantilever is attached by a diamond nitrogen-vacancy center under a strong magnetic field gradient and the cooling is assisted by a dynamical Stark-shift gate. Our scheme can effectively enhance the desired cooling efficiency by avoiding the off-resonant and unexpected carrier transitions, …
Single-spin detection is one of the important challenges facing the development of several new technologies, e.g. single-spin transistors and solid-state quantum computation. Magnetic resonance force microscopy with a cyclic adiabatic inversion, which utilizes a cantilever oscillations driven by a single spin, is a promising technique to solve this problem. We have studied the quantum dynamics of a single spin interacting with a quasiclassical cantilever. It was found that in a similar fashion to the Stern-Gerlach interferometer the quantum dynamics generates a quantum superposition of two qua…
We report the realization of dynamical localization in a strongly driven two-mode optomechanical system consisting of two coupled cantilevers. Due to the coupling, mechanical oscillations can transport between the cantilevers. However, by placing one of the cantilevers inside a harmonically oscillating optical trap, we demonstrate that mechanical oscillations become tightly bounded to the isolated cantilevers rather than propagate away at specific driving parameters. The effect of dynamical localization is employed to induce a conductor-to-insulator-like transition in the two-mode mechanical s…
We review the quantum theory of a single spin magnetic resonance force microscopy (MRFM). We concentrate on the novel technique called oscillating cantilever-driven adiabatic reversals (OSCAR), which has been used for a single spin detection (Dan Rugar, Talk on the 2004 IEEE NTC Quantum Device Technology Workshop). First we describe the quantum dynamics of the cantilever-spin system using simple estimates in the spirit of the mean field approximation. Then we present the results of our computer simulations of the Schrodinger equation for the wave function of the cantilever-spin system and of t…
We propose a simple model which describes the statistical properties of quantum jumps in a single-spin measurement using the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. Our computer simulations based on this model predict the average time interval between two consecutive quantum jumps and the correlation time to be proportional to the characteristic time of the magnetic noise and inversely proportional to the square of the magnetic noise amplitude.
When trapped atoms are illuminated by weak lasers, off-resonant transitions cause shifts in the frequencies of the vibrational-sideband resonances. These frequency shifts may be understood in terms of Stark-shifts of the individual levels or, as proposed here, as a vibrational Bloch-Siegert shift, an effect closely related to the usual (radio-frequency or optical) Bloch-Siegert shift and associated with rapidly oscillating terms when the Rotating Wave Approximation is not made. Explicit analytic expressions are derived and compared to numerical results, and the similarities and differences bet…
According to the Schiff theorem, the atomic electrons completely screen the atomic nucleus from an external static electric field. However, this is not the case if the field is time-dependent. Electronic orbitals in atoms either shield the nucleus from an oscillating electric field when the frequency of the field is off the atomic resonances or enhance this field when its frequency approaches an atomic transition energy. In molecules, not only electronic, but also rotational and vibrational states are responsible for the screening of oscillating electric fields. As will be shown in this paper,…
We consider a simple version of a cyclic adiabatic inversion (CAI) technique in magnetic resonance force microscopy (MRFM). We study the problem: What component of the spin is measured in the CAI MRFM? We show that the non-destructive detection of the cantilever vibrations provides a measurement of the spin component along the effective magnetic field. This result is based on numerical simulations of the Hamiltonian dynamics (the Schrodinger equation) and the numerical solution of the master equation.
This study demonstrates how the spin quantum dynamics of a single Fe atom adsorbed on Cu(001) can be controlled and manipulated by the vibrations of a nearby copper tip attached to a nano cantilever by virtue of the dynamic magnetic anisotropy. The magnetic properties of the composite system are obtained from \emph{ab initio} calculations in completely relaxed geometries and turned out to be dependent considerably on the tip-iron distance that changes as the vibrations set in. The level populations, the spin dynamics interrelation with the driving frequency, as well as quantum information rela…
