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The detected spectrum in the Unruh effect is Planckian for massless fields. The reason is that the latter display a linear dispersion relation. It is also well known that for massive fields, the detected spectrum in the Unruh effect would lose its Planckian profile. Remarkably, the relativistic Doppler shift approach to the Unruh effect shows that, just like with massive fields, fields with nonlinear dispersion relations also lead to a departure from a Planckian spectrum. The approach even applies to the case of modified Lorentz transformations. The big advantage of the approach, however, lies in the fact that it offers a very intuitive explanation for the reasons behind such results, and applies even to analogs of the Unruh effect. Detecting such a departure from thermality using water surface waves is very promising.

CAP Virtual Congress 2021

Revisiting the Unruh effect with modified dispersion relations

modified dispersion relations

relativistic doppler shift

unruh effect

Join us in exploring emergent themes in PER as a scholarly endeavor and as a research community!  Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?
Following the lead of AAPT for the summer meeting, PERC 20/20 was virtual. Enjoy browsing the content.

PERC SM 20

Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?

poster

**WELCOME TO THE 2021 CAP VIRTUAL CONGRESS UNDERLINE PLATFORM**

The CAP staff and our organizing and program committees are pleased to welcome you to our 2021 Congress filled with plenary talks, technical sessions/talks, student presentations and competition sessions, workshops, and several symposia offered by the CAP divisions and its partners.  

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Registered delegates should use the schedule button to call up the details of the session/event they wish to attend.  Each sessions includes a link to access the online platform where the event is taking place, either within Underline or through other Congress-related Zoom meetings.  

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We look forward to sharing this exciting week with you!


We prove that the state created via spontaneous parametric downconversion in a two-mode lossy cavity is a squeezed thermal state. We examine the case of generation in a side-coupled ring resonator.

In the context of quantum optics, two-mode squeezed states are routinely used as a source of continuous-variable (CV) entanglement for applications in the field of quantum information [1]. They can be generated via a nonlinear interaction such as spontaneous parametric downconversion (SPDC), where a strong coherent pump field interacts with a material that has a $\chi^{(2)}$ nonlinearity. The resulting squeezed light exhibits correlations between the quadratures of photons in the two modes.

In this work, we model the nonlinear generation of a squeezed state inside a lossy multimode cavity using the Lindblad master equation and show that the exact solution to this model is a two-mode squeezed thermal state, with time-dependent squeezing amplitude and thermal photon number in each mode. We also derive an analytic expression for the entanglement between the modes, and calculate the degree of entanglement in a side-coupled ring resonator. 

These results will be of use to researchers that are trying to optimize CV entanglement in lossy cavities when the losses of each mode are different.

[1] Samuel L Braunstein and Peter Van Loock. Quantum Information with Continuous Variables.Rev. Mod.Phys., 77:513, 2005.

Continuous-variable entanglement in a ring resonator: An analytic solution

Molecular dynamics simulations are, in principle, numerically exact, but severely restricted with respect to the accessible time- and length-scale of the system studied. Stochastic simulations offer an alternative modeling method that overcomes these limitations. Unfortunately, the relation between the properties of the original system and the parameters used in stochastic modeling is not always clear. We address this problem by studying the diffusion of a Brownian particle along a chain of coupled stochastic oscillators. We show that stochastic simulations of the Brownian particle alone may be in quantitative as well as in qualitative disagreement with the result of the full-scale molecular dynamics simulations. As a remedy, we propose to simulate a small part of the chain together with the Brownian particle, which now becomes ``dressed''. We introduce a recipe to perform the stochastic simulations of the part of the chain. We show that the diffusion coefficient of the Brownian particle in this type of stochastic modeling is practically the same as in the molecular dynamics simulations in a broad parameter range.

Brownian motion on a stochastic oscillator chain

Geometrical frustration arises in systems whose structures support multiple degenerate ground states. Artificial spin ice (ASI), has been built in diverse configurations which allows us to control frustration by experimentally tuning suitable parameters[1]. We present computational results on ASI systems consisting
of planar arrays of nanosized elongated ferromagnetic islands where geometrical frustration takes place at the vertices due to dipolar interactions between elements. To date, most studies have employed two-dimensional geometries in order to study magnetic charge dynamics, phase transitions, vertex-based frustration, and other interesting effects[2]. Recently, there has been a surge of interest in realizing three-dimensional artificial spin ice[3]. The use of a third dimension allows increased configurability and optimization of the magnetostatic interaction between different elements of the system. The work mentioned here concerns non-
equilibrium dynamics of a bilayer artificial spin ice structure consisting of two identical arrays separated by some distance and rotated at an angle between the two array axes. Introducing an angle between the layers enables the observation of novel, emergent phenomena as it changes the nature of the interactions between
the spins. We consider pinwheel variants of a square ice geometry for each
array[4]. Using different Monte Carlo techniques, we examine ground state ordering as a function of the interaction strength between layers for different relative orientations. Avalanche processes are also investigated and contrasted with those found in single-layer arrays.

References:
[1] RF Wang, C Nisoli, RS Freitas, J Li, W McConville, BJ Cooley, MS Lund, N Samarth, C Leighton, VH Crespi, et al. Artificial `spin ice' in a geometrically frustrated lattice of nanoscale ferromagnetic islands. Nature, 439(7074):303{306, 2006.
[2] Cristiano Nisoli, Vassilios Kapaklis, and Peter Schier. Deliberate exotic magnetism via frustration and topology. Nature Physics, 13(3):200{203, 2017.
[3] Gia-Wei Chern, Charles Reichhardt, and Cristiano Nisoli. Realizing three-dimensional artificial spin ice by stacking planar nano-arrays. Applied Physics Letters, 104(1):013101, 2014.
[4] R. Mac^edo, G. M. Macauley, F. S. Nascimento, and Robert L. Stamps. Apparent ferromagnetism in the pinwheel artificial spin ice. Physical Review B,
98(1):014437, 2018.

Investigation of the dynamics of twisted bilayer artificial spin ice structure

The discovery of time-reversal symmetry(TRS) breaking in elemental Re has ignited fresh interest in the Re based superconductors. The recent studies show that role of Re concentration and crystal symmetry is crucial in understanding the unconventional superconductivity of these compounds. Therefore, we studied two Re-based superconductors Re$_3$B (<var>TC</var> = 5.19 K) and Re$_7$B$_3$ 
(<var>TC</var> = 3.2 K) having a centrosymmetric and non-centrosymmetric crystal structure, respectively. In this talk, we will present a comprehensive study on superconducting properties of Re$_7$B$_3$ and Re$_3$B through specific heat, magnetic susceptibility, resistivity, and transverse and zero-field muon rotation/relaxation ($\mu$SR) experiments. This will include the temperature dependence of penetration depth using transverse-field $\mu$SR measurements, which will be used to determine the symmetry of the superconducting gap. To further explore these materials, we performed the zero-field $\mu$SR measurements, which show the evidence for TRS preserving superconducting state for both materials in the limits of our measurements.

$\mu$SR study of superconducting Re-B compounds

The Kitaev model on the honeycomb lattice recently attracted considerable attention. However, in candidate materials, other interactions are present, and 
among them the off-diagonal $\Gamma$ interaction has been particularly challenging. While several numerical studies on a minimal Kitaev-$\Gamma$ $(K\Gamma)$ model found multiple quantum disordered phases, definite conclusions on existence of quantum spin liquids remain elusive due to various numerical limitations. Here we present a classical phase diagram of the $K\Gamma$ model in the presence of the bond-anisotropy, which reveals intriguing competing phases and extended frustration. The stability of the classical phases to quantum fluctuations using a linear spin wave theory will be also discussed.

Extent of Frustration in the Classical Kitaev-$\Gamma$ Model

Dynamical backaction resulting from radiation pressure forces in optomechanical systems has proven to be a versatile tool for manipulating mechanical vibrations. Notably, dynamical backaction has resulted in the cooling of a mechanical resonator to its ground-state, driving phonon lasing, and observing the optical-spring effect. In certain magnetic materials, mechanical vibrations can interact with magnetic excitations (magnons) via the magnetostrictive interaction, resulting in an analogous magnon-induced dynamical backaction. This talk will discuss the direct observation of magnon-induced dynamical backaction and its effect on a spherical magnetic sample's mechanical vibrations. Moreover, dynamical backaction effects play a crucial role in many recent theoretical proposals; thus, our work provides the foundation for future experimental work perusing many of these novel theoretical proposals. foundation for future experimental work perusing many of these novel theoretical proposals.

Dynamical Backaction Magnomechanics

By engineering an anti-parity-time (anti-PT) symmetric cavity magnonics system with precise eigenspace controllability, we observe two different singularities in the same system. One type of singularity, the exceptional point (EP), is produced by tuning the magnon damping. Between two EPs, the maximal coherent superposition of photon and magnon states is robustly sustained by the preserved anti-PT symmetry. The other type of singularity, arising from the dissipative coupling of two antiresonances, is a zero-damping condition (ZDC). At the settings of ZDCs, the coupled system exhibits infinite discontinuities in the group delay. We find that both singularities coexist at the equator of the Bloch sphere, which reveals a unique hybrid state that simultaneously exhibits the maximal coherent superposition and slow light capability.

Unconventional singularity in anti-parity-time symmetric cavity magnonics

The classical Einstein-de Haas (EdH) effect [1] is a AC mechanical torque arising from a time rate of change of net magnetization, and represents the intrinsic relationship between magnetism and mechanical angular momentum. Nanofabrication of torque sensing devices is opening new avenues for exploration and applications of the EdH effect. The scale-up of resonance frequencies with continued miniaturization of mechanical torque sensing resonators enhances EdH torques, which increase linearly with drive frequency, relative to frequency-independent magnetic cross-product torques. Previously, miniaturized EdH experiments have been performed at the microscale using mechanical modes in the audio frequency range (13 kHz) [2]. The present work brings the measurements to radio frequencies. 

Single-crystal Yttrium Iron Garnet (YIG) disks with magnetic vortex ground states are mounted on nano-scale mechanical resonators with a torsional resonance mode close to 3 MHz. For DC bias fields below about 200 A/m the maximum cross-product torques remain smaller than the EdH torques [3]; no control of the field geometry to null cross-product torques is required. Quadrature lock-in measurements allow cross-product and EdH torque signals to be recorded simultaneously, owing to a 90$^{\circ}$ relative phase shift arising between the driving torques, and referenced to the phase of the driving field. The simultaneous measurement scheme enables determination of the magnetomechanical ratio, $g\prime$, without requiring separate experimental inputs. Results from measurements around the full vortex hysteresis loop, and comparisons with micromagnetic simulations of cross-product and EdH torques, also will be discussed.

[1] A. Einstein and W.J. de Haas, Proceedings - KNAW **18**, 696 (1915).

[2] T.M. Wallis, J. Moreland, and P. Kabos, Appl. Phys. Lett. **89**, 122502 (2006)

[3] K. Mori, M.G. Dunsmore, J.E. Losby, D.M. Jenson, M. Belov, and M.R. Freeman, Phys. Rev. B **102**, 054415 (2020)

The Einstein-de Haas Effect in Yttrium Iron Garnet at 3 MHz

Since the magnetic skyrmion is a topologically protected particle-like domain in the ferromagnetic film, it can survive under thermal agitations and shows Brownian motion. The skyrmion system can be an ideal platform to design unconventional computers like stochastic/Brownian computers. Therefore, investigation of the Brownian motion of the magnetic skyrmion is now the subject of scientific and technical interest [1,2].
In this talk, experimental proof of a non-vanishing x-velocity to y-coordinate correlation will be shown. The result is explained by the Thiele equation including a stochastic field [3,4]. Description of the phenomena introduces the gyro-diffusion constant [5] that is special for the diffusion of the chiral particles like skyrmions. The existence of the x-velocity to y-coordinate correlation also evidences the perpetual rotation motion of the skyrmion. Theory shows that the result does not conflict with the 2nd law of thermodynamics and the van Leeuwen theorem.
Acknowledgments 
The authors acknowledge Mr. Y. Jibiki of Osaka University, Dr. S. Auffret, Dr. C. Baraduc, and Dr. Hélèn Béa of Spintech, France for their initial contributions. The authors also acknowledge Dr. M. Oogane and Dr. K. Saito. This research and development work was supported by the ULVAC, Inc., the Ministry of Internal Affairs and Communications, Basic research S (20H05666) of JSPS, and CREST (Non-classical Spin project) of JST.
References
[1] Y. Jibiki et al., Appl. Phys. Lett. 117, 082402 (2020).
[2] L. Zhao et al., Phys. Rev. Lett. 125, 027206 (2020).
[3] A. Thiele et al., Phys. Rev. Lett. 30, 230 (1973).
[4] C. Schuette et al., Phys. Rev. B 90, 174434 (2014)
[5] E. Tamura et al. https://arxiv.org/abs/2005.04860.

Hidden diffusion and perpetual motion of the skyrmions

High-finesse optical nanocavities coupled with nanomechanical torque sensors have enabled highly sensitive and broadband readout of magnetic torques, from timescales involving quasi-static hysteresis response to radio-frequency magnetic susceptibility [1-3]. The extension of torque magnetometry to higher mechanical frequencies will grant further access to spin dynamics, including mechanical investigations of spin-lattice relaxation times.

For nanomechanical torque magnetometry measurements into radio frequencies, the contribution of the Einstein-de Haas (EdH) effect can become comparable to, and even exceed, the conventional magnetic torque (cross-product of magnetic moment and applied field) signal [4]. Extending sensitive optomechanical detection across a ladder of higher-order mechanical modes is a natural way to extract further information, through examination of the relative scaling of EdH and cross-product torques.

Sufficiently high-order mechanical modes have application to co-resonant detection of magnetic resonances. Magnetic vortex resonances intersecting the mechanical resonance spectrum will be described, and allow for the observation of dynamic vortex core interactions with magnetic inhomogeneities. 

[1] M. Wu et al. Nat. Nanotechnol. 12, 127 (2017).
[2] G. Hajisalem et al. New J. Phys. 21, 095005 (2019).
[3] J. Losby et al. J. Phys D. 51, 483001 (2018).
[4] K. Mori et al. Phys. Rev. B. 102, 054415 (2020).

Multi-frequency torque magnetometry: contribution of the Einstein-de Haas effect, and direct detection of overlapping magnetic and mechanical resonance modes

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