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Register a new userStability and dynamics of optically levitated dielectric disks in a Gaussian standing wave beyond the harmonic approximation
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Forces and torques exerted on dielectric disks trapped in a Gaussian standing wave are analyzed theoretically for disks of radius $2~mutext{m}$ with index of refraction $n=1.45$ and $n=2.0$ as well as disks of radius 200 nm with $n=1.45$. Calculations of the forces and torques were conducted both analytically and numerically using a discrete-dipole approximation method. Besides harmonic terms, third order ro-translational coupling terms in the potential energy can be significant and a necessary consideration when describing the dynamics of disks outside of the Rayleigh limit. The coupling terms are a result of the finite extension of the disk coupling to both the Gaussian and standing wave geometry of the beam. The resulting dynamics of the degrees of freedom most affected by the coupling terms exhibit several sidebands as evidenced in the power spectral densities. Simulations show that for Gaussian beam waists of $1-4~mutext{m}$ the disk remains stably trapped.
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Optically levitated nonspherical particles in vacuum are excellent candidates for torque sensing, rotational quantum mechanics, high-frequency gravitational wave detection, and multiple other applications. Many potential applications, such as detecting the Casimir torque near a birefringent surface, require simultaneous cooling of both the center-of-mass motion and the torsional vibration (or rotation) of a nonspherical nanoparticle. Here we report the first 5D cooling of a levitated nanoparticle. We cool the 3 center-of-mass motion modes and 2 torsional vibration modes of a levitated nanodumbbell in a linearly-polarized laser simultaneously. The only uncooled rigid-body degree of freedom is the rotation of the nanodumbbell around its long axis. This free rotation mode does not couple to the optical tweezers directly. Surprisingly, we observe that it strongly affects the torsional vibrations of the nanodumbbell. This work deepens our understanding of the nonlinear dynamics and rotation coupling of a levitated nanoparticle and paves the way towards full quantum control of its motion.
A nitrogen-vacancy (NV$^-$) center in a nanodiamond, levitated in high vacuum, has recently been proposed as a probe for demonstrating mesoscopic center-of-mass superpositions cite{Scala2013, Zhang2013} and for testing quantum gravity cite{Albrecht2014}. Here, we study the behavior of optically levitated nanodiamonds containing NV$^-$ centers at sub-atmospheric pressures and show that while they burn in air, this can be prevented by replacing the air with nitrogen. However, in nitrogen the nanodiamonds graphitize below $approx 10$ mB. Exploiting the Brownian motion of a levitated nanodiamond, we extract its internal temperature ($T_i$) and find that it would be detrimental to the NV$^-$ centers spin coherence time cite{Toyli2012}. These values of $T_i$ make it clear that the diamond is not melting, contradicting a recent suggestion cite{Neukirch2015}. Additionally, using the measured damping rate of a levitated nanoparticle at a given pressure, we propose a new way of determining its size.
The entanglement dynamics of two remote qubits is examined analytically. The qubits interact arbitrarily strongly with separate harmonic oscillators in the idealized degenerate limit of the Jaynes-Cummings Hamiltonian. In contrast to well known non-degenerate RWA results, it is shown that ideally degenerate qubits cannot induce bipartite entanglement between their partner oscillators.
It is well known that the Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space that is twice as large as in the corresponding classical system. We construct several generalizations of this approach that include non-Gausssian wave packets. These generalizations lead to the further extension of the phase space while retaining the Hamilton structure of the equations of motion. We compare the Gaussian dynamics with these non-Gaussian extensions for a particle with the quartic potential.
Laguerre-Gaussian (LG) beam has orbital angular momentum (OAM). A particle trapped in an LG beam will rotate about the beam axis, due to the transfer of OAM. The rotation of the particle is usually in the same direction as that of the beam OAM. However, we discovere that when the LG beam is strongly focused, the rotation of the particle and the beam OAM might be in the opposite direction. This anomalous effect is caused by the negative torque on the particle exerted by the focused LG beam, which is similar to the optical pulling force in the linear case. We calculated the scattering force distribution of a micro-particle trapped in an optical tweezers formed by the strongly focused LG beam, and showed that there exist stable trajectories of the particle that controlled by the negative torque. We proposed several necessary conditions for observing the counter-intuitive trajectories. Our work reveals that the strongly trapped micro-particle exhibits diversity of motion patterns.
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