Stern-Gerlach and/or matter-wave interferometry has garnered significant interest amongst members of the scientific community over the past few decades. Early theoretical results by Schwinger et al. demonstrate the fantastic precision capabilities required to realize a full-loop Stern-Gerlach interferometer, i.e., a Stern-Gerlach setup that houses the capability of recombining the split wave-packets in both, position and momentum space over a certain characteristic interferometric time. Over the years, several proposals have been put forward that seek to use Stern-Gerlach and/or matter-wave interferometry as a tool for a myriad of applications of general interest, some of which include tests for fundamental physics (viz., quantum wave-function collapse, stringent tests for the Einstein equivalence principle at the quantum scale, breaking the Standard Quantum Limit (SQL) barrier, and so forth), precision sensing, quantum metrology, gravitational wave detection and inertial navigation. In addition, a large volume of work in the existing literature has been dedicated to the possibility of using matter-wave interferometry for tests of quantum gravity. Inspired by the developments in this timely research field, this Perspective attempts to provide a general overview of the theory involved, the challenges that are yet to be addressed and a brief outlook on what lays ahead.
A quantitative description of the violation of the second law of thermodynamics in relatively small classical systems and over short time scales comes from the fluctuation-dissipation theorem. It has been well established both theoretically and experimentally, the validity of the fluctuation theorem to small scale systems that are disturbed from their initial equilibrium states. Some experimental studies in the past have also explored the validity of the fluctuation theorem to nonequilibrium steady states at long time scales in the asymptotic limit. To this end, a theoretical and/or purely numerical model of the integral fluctuation theorem has been presented. An approximate general expression for the dissipation function has been derived for accelerated colloidal systems trapped/confined in power-law traps. Thereafter, a colloidal particle trapped in a harmonic potential (generated by an accelerating one-dimensional optical trap) and undergoing Brownian motion has been considered for the numerical study. A toy model of a quartic potential trap in addition to the harmonic trap has also been considered for the numerical study. The results presented herein show that the integral fluctuation theorem applies not only to equilibrium steady state distributions but also to nonequilibrium steady state distributions of colloidal systems in accelerated frames of reference over long time scales.
In the original article, two references were not cited. These are as follows: 20. Marshman RJ, Mazumdar A, Bose S. Locality and entanglement in table-top testing of the quantum nature of linearized gravity. Phys Rev A (Coll Park) (2020) 101: 052110.
A Stern-Gerlach interferometer uses a magnetic field gradient to split particle wave functions into spatially separated wave-packets according to their respective spin projections. Over the years, quite a few proposals have been put forward by various groups to exploit this effect in order to create stable macroscopic spatial superpositions between micron-sized neutral test masses over appreciably long time scales. One such proposal put forward by Bose et al. and co-workers in 2017 uses this idea to show that two masses cannot be gravitationally entangled if not for the presence of a quantum coherent mediator (i.e., through spin correlation measurements between two quantum spins, each embedded in a test mass, they seek to demonstrate that gravity can act as a quantum coherent mediator [see [1]]. This primarily involves cooling the test mass to the ground state of a harmonic trap, thereby releasing it in a Stern-Gerlach interferometer. A key aspect of this approach involves the measure of the visibility of the SG-interferometer, a quantity that provides an estimate of the degree of spin coherence that is conserved over the total interferometric time after the wavepackets are combined in both, position and momentum space. A successful implementation of this idea however requires the knowledge of several experimental parameters, some of which include the temperature to which the test mass must be cooled initially, the admissible experimental errors in the measure of the phase-space observables (i.e., spatial and momentum splitting between the wave-packets with respect to the initial position and momentum uncertainties of the test mass 1 in the ground state of the harmonic trap) and the total time-of-flight of the wave-packets in the interferometer. To this end, we present a rigorous mathematical analysis for the visibility in a general SG interferometer for non-squeezed and squeezed thermal coherent states of the Quantum harmonic oscillator. Additionally, by considering suitable experimental errors in the measure of the phase-space variables and subject to the desired accuracy in the measure of the visibility, we derive constraints on the temperature of the initially prepared wave-packet of the test mass for both, the non-squeezed and squeezed coherent states. We show that for wave-packet split sizes of the order of microns, masses of the order of 10 −14 -10 −15 kg can be used to realize such a proposal in practice for time intervals as high as 0.5 seconds. Our results show that for the squeezed case, the temperatures required can be scaled up by several orders of magnitude (as opposed to the non-squeezed case) if one considers a squeezing in the momentum space of the initially prepared wave-packet.
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