Recently we showed that quantum systems in orbit around a massive body may be compared to ground clocks to test the gravitational Aharonov-Bohm effect. To be sensitive, orbits must have non-zero eccentricity, so geometric phase effects related to the time varying gravitation potential will be present. Since the quantum system will be in free-fall, by the equivalence principle, the quantum system is locally screened from the gravitational field. However, the time varying gravitational potential will change the energy levels of the quantum system and develop side bands, which are harmonics of the orbit frequency and is the signature of the scalar Aharonov-Bohm effect. Experiments that have the potential to measure such geometric phases include atomic clocks in space, such as the ACES mission, as well as other missions that propose optical clocks in space. Also, worth investigating is the possible use of data from Galileo clocks with non-zero eccentricity.

In this article, we review a new approach to the scalar Aharonov-Bohm effect for both the electromagnetic and gravitational interaction. For both interactions a quantum system is placed in a time-dependent electromagnetic or gravitational potential, but with no force (spatial derivative of the potential) acting on the quantum system. Nevertheless, we show that the energy levels of the quantum system develop side bands which can be detected as the signature of this version of the scalar Aharonov-Bohm effect. We briefly look at the specific experimental setups required to detect the energy side bands.

Radio-frequency (RF) cavities, previously employed in particle physics, quantum computing, and gravitational wave research, offer unique advantages in terms of sensitivity and non-invasiveness as a method of sensing motion in both macroscopic and microscopic systems. This research aims to address how an RF cavity can effectively detect and characterize the low-frequency vibratory motion of a room-temperature mm-scale levitated particle. In this case, the particle in question is a diamagnetically levitated slab of highly oriented pyrolytic graphite. Cavity-based identification of the slab’s rigid-body modes is substantiated by calculations of the force acting on the particle and validated through slow-motion video object tracking. We find that this system can accurately measure oscillations in all six center-of-mass degrees of freedom. Calculations indicate that this system could potentially detect forces on the scale of tens of femto-Newtons and center of mass displacements of less than 10 nm. This work provides a non-invasive method of conducting position and vibration measurements in the field of levitodynamics without the ultra-cold temperatures or bulky precision laser setups that superconducting quantum interference devices and conventional interferometric methods utilize.

We investigate the gravitational Aharonov-Bohm effect by placing a quantum system in free fall around a gravitating body, e.g., a satellite orbiting the Earth. Since the system is in free fall, by the equivalence principle, the quantum system is local in flat, gravity free space-time-it is screened from the gravitational field. For a slightly elliptical orbit, the gravitational potential will change with time. This leads to the energy levels of the quantum system developing sidebands which is the signature for this version of the AharonovBohm effect. This contrasts with the normal signature of the Aharonov-Bohm effect of shifting of interference fringes.

A novel version of the electric Aharonov-Bohm effect is proposed where the quantum system which picks up the Aharonov-Bohm phase is confined to a Faraday cage with a time varying, spatially uniform scalar potential. The electric and magnetic fields in this region are effectively zero for the entire period of the experiment. The observable consequence of this version of the electric Aharonov-Bohmn effect is to shift the energy levels of the quantum system rather than shift the fringes of the 2-slit interference pattern. We show a strong mathematical connection between this version of the scalar electric AB effect and the AC Stark effect.

The levitation of a macroscopic object within a superconducting resonator provides a unique and novel platform to study optomechanics, quantum information, and gravitational wave detection. Existing mirror-method and single-loop models for calculating magnet levitation are insufficient for predicting the position and motion of the levitated magnet. If the cavity-magnet interaction is modeled using a large number of smaller surface current loops, one can quantitatively model the dynamics of the levitation of the magnet within the cavity. The magnet's most-likely position and orientation can be predicted for non-trivial cavity geometries and cavity orientations. Knowing the potential energy landscape within the cavity configuration also provides a means to estimate the resonant mechanical frequencies at which the levitated magnet vibrates, and enables tailoring the cavity design for specific outcomes.

We report on the behavior of a superconducting microwave cavity containing levitated permanent magnets having a range of magnet strengths. By observing the changes in the cavity’s loaded quality factor and resonance frequency as functions of temperature and magnet remanence, we gain an understanding of the transient motion of the magnet as well as its steady-state levitation height when the temperature drops below 1 K. Experimental measurements of Meissner-effect levitation within a 10-GHz superconducting aluminum coaxial quarter-wave stub cavity are performed for a sequence of identically shaped millimeter-scale neodymium magnets having varying strengths. Magnet levitation within the cavity is accompanied by both gradual and abrupt shifts in the resonance frequency (with a height sensitivity as large as 400 MHz/mm) as well as changes in the total quality factor (8%–17%) as a function of temperature during the superconducting transition of the aluminum cavity. Prior to magnet motion and levitation, ${Q}$ of the cavity changes quadratically with temperature, as expected, as the walls of the cavity undergo the superconducting transition. We observe, however, a deviation from the quadratic trend, which is attributable to magnet movement within the cavity. Such an electromechanical system is a transducer between mechanical and microwave oscillators enabling coupling of low-frequency mechanical motion of the magnet to other quantum objects, such as magnons and transmons, which are used for sensing and quantum information processing.

Levitation refers to free flotation, where the levitated object is suspended freely, against gravity without any physical contact. Among many levitation, magnetic levitation due to a finite-sized type-I superconductor was demonstrated and characterized. Here, we have developed a model by extending the two-loop method to calculate the levitation height for magnetic levitation within the superconducting microwave cavity and is compared with widely used mirror and finite-size superconductor method. The models were used to calculate the levitation height from the center and edge of the superconductor for magnet with strength 0.1 - 2.0 T. We observed a large discrepancy between the models for the edge levitation where our model underestimate the levitation height by 40-95%. Furthermore, in contrast to other models, our model has shown a superior capacity to calculate the levitation height at any location on the superconductor

The low energy losses in the superconducting magnetic levitation make it attractive for exciting applications in physics. Recently, superconducting magnetic levitation has been realized as novel mechanical transduction for the individual spin qubit in the nitrogen-vacancy center [1]. Furthermore, the Meissner has been proposed for the study of modified gravitational wave detection [2]. Meissner levitation within the microwave cavity could open avenues for the novel cavity optomechanical system, readout for quantum object such as the transmon, and magnon, gravitational wave detection, and magnetomechanics [3]. This work characterized magnetic levitation within a microwave. It also discusses possibilities, challenges, and room temperature and cryogenic experiments of the cavity-magnet system.

Magnetic levitation has been demonstrated and characterized within the coaxial microwave cavity [1,2]. A permanent neodymium magnet is levitated from the edge of the finite-size superconductor [3,4]. One challenge is to develop a better method to calculate levitation height [5]. This paper compares three models, the Mirror method, finite-size superconductor, and two-loop model, for the levitation height calculation. The limitations and advantages of each model are discussed in detail.

The Casimir force was predicted in 1948 as a force arising between macroscopic bodies from the zero-point energy. At finite temperatures, it has been shown that a thermal Casimir force exists due to thermal rather than zero-point energy and there are a growing number of experiments that characterize the effect at a range of temperatures and distances. In addition, in the rapidly evolving field of cavity optomechanics, there is an endeavour to manipulate phonons and enhance coherence. We demonstrate a way to realize a Casimir spring and engineer dilution in macroscopic optomechanics, by coupling a metallic SiN membrane to a photonic re-entrant cavity. The attraction of the spatially localized Casimir spring mimics a non-contacting boundary condition, giving rise to increased strain and acoustic coherence through dissipation dilution. This provides a way to manipulate phonons via thermal photons leading to ‘in situ’ reconfigurable mechanical states, to reduce loss mechanisms and to create additional types of acoustic nonlinearity—all at room temperature. An optomechanical cavity comprising a re-entrant cavity and membrane resonators can be tuned in and out of the Casimir regime. At the transition between the two regimes, the mechanical resonators exhibit a change in stiffness—the Casimir spring.

Levitated systems are desirable due to reduced clamping losses and reduced thermal contact. These advantageous properties have been exploited in optomechanics to achieve ultra-strong coupling between the mechanical mode and the electromagnetic mode. Such schemes provide an opportunity for the quantum manipulation of a macroscopic system. In this letter, we report the first successful experiments with a levitated millimeter-scale neodymium magnet within a centimeter-scale superconducting aluminum coaxial quarter-wave stub cavity. The magnet levitated near the top of the stub, where the electric field is concentrated, perturbs the electric field distribution allowing for small perturbations in the magnet's position to be detected through shifts in the resonance frequency. Resonance spectra are collected via a vector network analyzer (VNA) between temperatures of 5 K and 50 mK revealing movement of the magnet inside of the cavity. Room temperature measurements and finite element calculations are done to calculate the shift in frequency for various positions of the magnet, and an experimentally measured 100 MHz upshift when transitioning into a superconducting state confirms levitation with remanences up to 140 times stronger than the critical field of the aluminum. We achieve levitation heights of 1 - 1.8 mm. We investigate the dependence of levitation height and levitation temperature on the strength of the magnet and, surprisingly, we observe that the levitation temperature and height both increase with permanent magnet strength. Our work describes a novel macroscopic mechanical system capable of sensing and transducing forces, thus allowing for the coupling of disparate classical and quantum systems.

We report on the magnetic levitation of a millimeter-sized neodymium permanent magnet within the interior of a superconducting radio frequency (SRF) cavity. To the best of our knowledge, this is the first experimental work on levitating a magnet within an SRF cavity. The cavity is a coaxial quarter-wave microwave resonator made from 6061 aluminum, having a resonance frequency of 10 GHz and a loaded Q of 1400. The cylindrical magnet (N50) has a height of 1 mm, a diameter of 0.75 mm, a mass of 4 mg, and a remanence of 1.44 T. This produces a peak magnetic field 140 times greater than the critical field of aluminum. The magnet is placed either on the top of the coaxial portion of the cavity or on the cavity floor before cooling it below the superconducting transition temperature of aluminum. The coaxial mode's resonance frequency shifts as a function of the levitation height of the magnet and gives an idea of the magnet's position and mechanical motion. We observe a transition at a temperature of 650 mK where the Meissner effect levitates the magnet as the material beneath the magnet becomes superconducting. The magnet is levitated to a height of 2.5 mm above the surface of the cavity stub, which is a sufficient separation for the field strength of the magnet at the surface of the stub to be less than the critical field strength of the superconducting aluminum. We measure a 120 MHz upshift in the cavity resonance as the magnet is levitated from the top of the stub and 15 MHz downshift as it levitates from the floor of the cavity. Our measurements are consistent over several heating and cooling cycles. Our work provides a path towards a novel optomechanical system.

We experimentally demonstrate four-wave mixing (FWM) in a triple-core microstructure fiber for a pump wavelength of 1064 nm. We study the transition between the case where FWM happens primarily in a single core and the case where FWM is distributed among multiple cores. The effective nonlinear coefficient is reduced by a factor of 3 (the number of cores) for distributed-core FWM compared with that for single-core FWM. This effect also leads to a three-fold reduction in the FWM bandwidth for distributed-core FWM. We report on the wavelength and polarization dependence of the core-to-core coupling length, and how those phenomena produce power-dependent coupling among the cores. These are the first reported experimental measurements of FWM in a 3-core microstructure fiber providing critical information for their use as nonlinear optical devices.

Photonics includes light generation, transmission, modulation, amplification, storage, and detection. It includes both classical and quantum physical concepts. Photonics expands on traditional optics to include a much broader range of frequencies extending from microwave frequencies well into the ultraviolet spectrum. Waveguides, including optical fibers, enable the spatial confinement of a beam in a well-defined volume and the transmission of light from one location to another. The fiber optic has a round cross-section, rather than square. This means that, for a large diameter cable, there can be many different transverse modes corresponding to a single wavelength. The types were perhaps introduced to prevent accidental connection between physical contact and angled physical contact connectors, but both kinds come with both key widths. The width difference is too small to see by eye and is truly an annoyance.

In this paper, we report on simulations of two types of high-Q 3-dimensional cavities: cylindrical TE011 and coaxial quarter-wave stub. We investigate the dependence of Q on the practical implementation tolerances of gaps between components, shape imperfections, and frequency tuning strategies. We find that cylindrical cavities can maintain high Q for designs that include frequency tuning and mechanical elements, provided extraordinary care is taken with shape and gap tolerance during construction and assembly. Coaxial stub cavities can be made with variable frequency while maintaining high Q, but they require more creativity to include a mechanical element. Finally, we report on a coaxial stub cavity, incorporating a conically shaped stub that confines the electric field near the stub’s tip, thus enhancing field–matter interactions near the tip.

We describe a simple and intuitive parametric oscillator apparatus which is suitable for a classroom demonstration or an upper-division laboratory. In order to facilitate the incorporation of this apparatus into the physics curriculum, we provide the learning objectives for an upper-division physics laboratory experiment. We present typical experimental data illustrating the main features of parametric oscillators including oscillation threshold, frequency shifting at large amplitude and bistability. Our experiments and theory emphasize identifying the lowest-order threshold for oscillation in terms of the modulation depth and quality factor. This experiment provides a foundation for understanding current research such as that in quantum opto-mechanics and nonlinear dynamics.

An optoelectronic oscillator (OEO) generates a spectrally pure and ultra-stable radio frequency signal from a continuous wave laser source (Yao et al. 2004). In a conventional electrical oscillator, the energy storage capacity is limited, which compromises stability of the signal. To address this issue, Yao and Maleki invented the optoelectronic oscillator in 1996. This novel oscillator uses low-loss optical fiber to extend the length of the oscillator and thereby increases the amount of energy that can be stored (Madjar & Tibor 2006). Due to this additional energy storing component in the system, the purity and stability of the signal increase significantly. Following their invention, many modifications have been made over the years to improve the frequency stability of OEOs (lower phase noise and timing jitter). This review article discusses some of those key developments and then introduces some ongoing work devoted to understanding the impact of using electrical filters with Q >109.

Three-dimensional radio frequency cavities demonstrate excellent frequency selectivity and, as such, are known for their use in RF filters. These cavities have potential applications in quantum information science, precision displacement metrology, and quantum electrodynamics. Additionally, coupled cavities that form a spectral doublet allow for parametric gain when incorporating mechanical elements. Here, we investigate normal-mode splitting in a pair of quarter-wave stub microwave cavities at room temperature and cryogenic environments in order to identify coupling mechanics for normal and superconducting systems. Superconducting quarter-wave stub cavities with a resonant frequency of 10 GHz are made from reactor-grade niobium and exhibit Q ranging from 105 to 109. We varied cavity-to-cavity coupling to observe several normal-mode splittings of increasing peak separation until we observed a mode crossing. The minimum observed peak separation was 7 MHz for room temperature tests and 200 kHz for cryogenic tests. We also report on values of an intrinsic quality factor for the tuning cavity as a dielectric rod is translated along its symmetry axis. The realization of coupled superconducting radio frequency (SRF) cavities of this type is a necessary step toward implementation of parametric SRF-mechanical gain.