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arXiv:2007.10065 · Physical Review Letters

Quantum Persistent Tennis Racket Dynamics of Nanorotors

Yue Ma, Kiran E. Khosla, Benjamin A. Stickler, M. S. Kim

Published Jul 31, 2020• 38 citations
arXivHTMLPDF

Abstract

Classical rotations of asymmetric rigid bodies are unstable around the axis of intermediate moment of inertia, causing a flipping of rotor orientation. This effect, known as the tennis racket effect, quickly averages to zero in classical ensembles since the flipping period varies significantly upon approaching the separatrix. Here, we explore the quantum rotations of rapidly spinning thermal asymmetric nanorotors and show that classically forbidden tunneling gives rise to persistent tennis racket dynamics, in stark contrast to the classical expectation. We characterize this effect, demonstrating that quantum coherent flipping dynamics can persist even in the regime where millions of angular momentum states are occupied. This persistent flipping offers a promising route for observing and exploiting quantum effects in rotational degrees of freedom for molecules and nanoparticles.

DOI
10.1103/physrevlett.125.053604

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Classical rotations of asymmetric rigid bodies are unstable around the axis of intermediate moment of inertia, causing a flipping of rotor orientation. This effect, known as the tennis racket effect, quickly averages to zero in classical ensembles since the flipping period varies significantly upon approaching the separatrix. Here, we explore the quantum rotations of rapidly spinning thermal asymmetric nanorotors and show that classically forbidden tunneling gives rise to persistent tennis racket dynamics, in stark contrast to the classical expectation. We characterize this effect, demonstrating that quantum coherent flipping dynamics can persist even in the regime where millions of angular momentum states are occupied. This persistent flipping offers a promising route for observing and exploiting quantum effects in rotational degrees of freedom for molecules and nanoparticles.
The rotation of a nanoparticle in a quantum system has many applications, from theory to experiments. This paper will treat nanoparticle rotational dynamics for spin-embedded nanorotors. We will model it as a rigid body that properly treats the rotation in the coframe of the nanorotor in the presence of external fields. Besides rotation, we will further investigate how to create large spatial superpositions in the inhomogeneous external magnetic field, such as in the case of the Stern-Gerlach apparatus. The spin-embedded nanorotors play a crucial role in creating matter-wave interferometers through their spin and external magnetic field interaction Hamiltonian. We aim to provide a holistic interpretation of the dynamics of three Euler angles, their quantum evolution, and the nanorotor's spatial motion in a Stern-Gerlach-type setup, where we will consider one-full-loop interferometry. We will then study how the quantum evolution of all the Euler angles leads to a spin coherence loss upon interference and what manifests the Einstein-de Haas effect in an external magnetic field. In particular, we show that by imparting rotation along the direction of the magnetic field, we can stabilize the nanorotor's libration mode. We will also extend our analysis to a case where the initial state of the libration mode is thermal and discuss the contrast loss due to interference of the nanorotor upon one-loop completion.
The intrinsically nonlinear rotation dynamics of rigid bodies offer unprecedented ways to exploit their quantum motion. In this Letter, we devise a rotational analog of Mach-Zehnder interferometry, which allows steering symmetric rotors from fully aligned to completely antialigned. The scheme uses a superposition of four distinct orientations, emerging at the eighth of the quantum revival time, whose interference can be controlled by a weak laser pulse. We develop a semiclassical model of the effect and demonstrate that it persists even in presence of imperfections and decoherence.
A molecular rotor mechanism is proposed to explain weak magnetic field effects in biology. Despite being nanoscale (1 nm), this rotor exhibits quantum superposition and interference. Analytical modeling shows its quantum dynamics are highly sensitive to weak, but not strong, magnetic fields. Due to its enhanced moment of inertia, the rotor maintains quantum coherence relatively long, even in a noisy cellular environment. Operating at the mesoscopic boundary between quantum and classical behavior, such a rotor embedded in cyclical biological processes could exert significant and observable biological influence.
Abstract Controlling the motion of nanoscale objects at the quantum limit promises opportunities to test fundamental quantum physics and advances in quantum sensing. Rotational motion is of particular interest, as its nonlinear dynamics in a compact, closed configuration space provides access to phenomena such as rotational interferometry, tunnelling between angular configurations and quantum-enhanced torque sensing. A key requirement for such experiments is the capability to trap nanorotors and cool their orientation close to the two-dimensional librational quantum ground state. When rotational motion is confined in a harmonic potential, it becomes librational. Here we demonstrate that coherent scattering into a high-finesse cavity enables the ground-state cooling of two orthogonal librational modes of an optically levitated SiO 2 nanoparticle. Using a laser-induced desorption loading technique, we trap and cool several dimers and trimers of silica nanospheres to their respective ground states, all within a single day. The simultaneous cooling of both librational degrees of freedom allows us to align an individual nanorotor with respect to a space-fixed axis with an angular precision better than 20 µrad—close to the quantum-mechanical zero-point fluctuations.
The free translational dynamics of an n-body quantum system has many applications, e.g. in molecular and nuclei systems, where it is common to classify the degrees of freedom of the system in 3 rotational and 3n - 6 shape coordinates. It is known that there exists an interaction between the shape and orientation degrees of freedom. In particular, changes of the shape could induce an orientation change. In this work, it is shown a rotating quantum system which does not deform its shape probability density and with vanishing angular momentum. The orientation change is monitored with a localized orientation wavefunction. We characterize the localized wavefunctions and study their evolution under a rigid rotor-like Hamiltonian, concluding that this kind of wavefunctions may rotate by their own.
A theoretical framework is developed to study a magnetically levitated nanomagnet in the quantum regime. The system is very rich due to the interaction between its degrees of freedom: position, orientation, and magnetization. In particular, the Einstein--de Haas effect, namely the coupling between the magnetization and the angular momentum of the object, plays a dramatic role. This work sheds new light on one of the few unsolved problem in quantum mechanics, the rigid rotor with a spin. At the same time, it opens up the possibility to model the dynamics of a single magnetic domain nanoparticle in a magnetic trap, an interesting new scenario for future experiments.