Uncertainty-principle noise in vacuum-tunneling transducers

Abstract

The fundamental sources of noise in a vacuum-tunneling probe used as an electromechanical transducer to monitor the location of a test mass are examined using a first-quantization formalism. We show that a tunneling transducer enforces the Heisenberg uncertainty principle for the position and momentum of a test mass monitored by the transducer through the presence of two sources of noise: the shot noise of the tunneling current and the momentum fluctuations transferred by the tunneling electrons to the test mass. We analyze a number of cases including symmetric and asymmetric rectangular potential barriers and a barrier in which there is a constant electric field. Practical configurations for reaching the quantum limit in measurements of the position of macroscopic bodies with such a class of transducers are studied

New reference books on magnetic properties of matter

“…Thus, we expect our results to be important to study the forces that act, for example, between the tip and the substrate of a scanning tunnelling microscope (STM) or an atomic force microscope [29,30]. Related calculations in 1D have been employed to quantify the quantum position and momentum uncertainties of the STM [22,23] and to study the statistics of electromechanical fluctuations in low-dimensional conductors [31]. We discussed how our results may be employed to calculate the surface energy of conductors without having to subtract total energies.…”

“…Furthermore, the phase space available right at the Fermi energy is null, due to the prefactor κ 2 F − κ 2 in equation (15), so the contributing electrons have a slightly larger decay constant (i.e., smaller range) than those at the Fermi level. This prefactor is absent in 1D calculations [22,23].…”

“…We express the momentum flux in terms of Green's function of the system, which we evaluate by means of a scattering method involving amplitude reflection coefficients [19,20]. This method yields an expression for the tunnelling force with a structure that is essentially identical to Lifshitz's formula [21] and which has not been uncovered by previous related calculations [22,23]. We first perform the calculation for a one-dimensional system.…”

Amplification phenomena of Casimir force fluctuations on close scatterers coupled via a coherent fermionic fluid

“…The non-equilibrium force given in Eq. (14) represents the pressure exerted by the electron wind generated by the voltage bias V b and provides a positive force on the scatterer when the applied voltage is negative. An expression similar to Eq.…”

Quantum Limit in Resonant Vacuum Tunnelling Transducers

“…A variation of the distance between the test mass and a tip changes the tunnelling current and whenever small fractions of the current are appreciable, corresponding displacements of the test mass, which are small fractions of the De Broglie wavelength of the tunnelling electrons, are also detectable. The relevance of this new class of transducers has been emphasized especially concerning detection of gravitational waves using bar antennae [1,2], design of quantum standard of current in metrology [3] and study of quantum-mechanical noise at the mesoscopic scale [4].Vacuum tunnelling transducers are intrinsically quantum limited [5]. The small output capacitance allows to neglect the back-action noise due to the amplifier following the transducer in the detection chain with respect to the quantum uncertainties coming from the tunnelling process in itself.…”