The control of levitated nano- and micro-objects in vacuum—which capitalizes on scientific achievements in the fields of atomic physics, control theory, and optomechanics—is of considerable interest. ...The ability to couple the motion of levitated systems to internal degrees of freedom, as well as to external forces and systems, provides opportunities for science and technology. Attractive research directions, ranging from fundamental quantum physics to commercial sensors, have been unlocked by the many recent experimental achievements, including motional ground-state cooling of an optically levitated nanoparticle. Here we review the status, challenges, and prospects of levitodynamics, the multidisciplinary research area devoted to understanding, controlling, and using levitated nano- and micro-objects in vacuum.
We demonstrate a new mechanical transduction platform for individual spin qubits. In our approach, single micromagnets are trapped using a type-II superconductor in proximity of spin qubits, enabling ...direct magnetic coupling between the two systems. Controlling the distance between the magnet and the superconductor during cooldown, we demonstrate three-dimensional trapping with quality factors around 1×10^{6} and kHz trapping frequencies. We further exploit the large magnetic moment to mass ratio of this mechanical oscillator to couple its motion to the spin degrees of freedom of an individual nitrogen vacancy center in diamond. Our approach provides a new path towards interfacing individual spin qubits with mechanical motion for testing quantum mechanics with mesoscopic objects, realization of quantum networks, and ultrasensitive metrology.
We study the generation and evolution of entanglement between two qubits coupled through one-dimensional waveguide modes. By using a complete quantum electrodynamical formalism we go beyond the ...Markovian approximation. The diagonalization of the Hamiltonian is carried out, and a set of quasi-localized eigenstates is found. We show that when the qubit-waveguide coupling is increased, the Markov approximation is no longer valid, and the generation of entanglement is worsened.
Recently, we proposed a way to engineer a flexible acoustomechanical coupling between the center-of-mass motion of an isolated micromagnet and one of its internal acoustic phonons by using a magnon ...as a passive mediator C. Gonzalez-Ballestero, J. Gieseler, and O. Romero-Isart, Phys. Rev. Lett. 124, 093602 (2020). In our approach, the coupling is enabled by the strong magnetoelastic interaction between magnons and acoustic phonons which originates from the small particle size. Here, we substantially extend our previous work. First, we provide the full theory of the quantum acoustomagnonic interaction in small micromagnets and analytically calculate the magnon-phonon coupling rates. Second, we fully derive the acoustomechanical Hamiltonian presented in Gonzalez-Ballestero et al. Finally, we extend our previous results for the fundamental acoustic mode to higher-order modes. Specifically, we show the cooling of the center-of-mass motion with a range of internal acoustic modes. Additionally, we derive the power spectral densities of the center-of-mass motion which allow us to probe the same acoustic modes.
We propose to use chirped pulses propagating near a band gap to remotely address quantum emitters. We introduce a particular family of chirped pulses that dynamically self-compress to subwavelength ...spot sizes during their evolution in a medium with a quadratic dispersion relation. We analytically describe how the compression distance and width of the pulse can be tuned through its initial parameters. We show that the interaction of such pulses with a quantum emitter is highly sensitive to its position due to effective Landau-Zener processes induced by the pulse chirping. Our results propose pulse engineering as a powerful control and probing tool in the field of quantum emitters coupled to structured reservoirs.
We theoretically study quantum size effects in the magnetic response of a spherical metallic nanoparticle (e.g., gold). Using the jellium model in spherical coordinates, we compute the induced ...magnetic moment and the magnetic susceptibility for a nanoparticle in the presence of a static external magnetic field. Below a critical magnetic field the magnetic response is diamagnetic, whereas above such field the magnetization is characterized by sharp, steplike increases of several tenths of Bohr magnetons, associated with the Zeeman crossing of energy levels above and below the Fermi sea. We quantify the robustness of these regimes against thermal excitations and finite linewidth of the electronic levels. Finally, we propose two methods for experimental detection of the quantum size effects based on the coupling to superconducting quantum interference devices.
Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two methods for the numerical ...evaluation of pfaffians. The first is tridiagonalization based on Householder transformations. The main advantage of this method is its numerical stability that makes unnecessary the implementation of a pivoting strategy. The second method considered is based on Aitkenʼs block diagonalization formula. It yields to a kind of LU (similar to Choleskyʼs factorization) decomposition (under congruence) of arbitrary skew-symmetric matrices that is well suited both for the numeric and symbolic evaluations of the pfaffian. Fortran subroutines (FORTRAN 77 and 90) implementing both methods are given. We also provide simple implementations in Python and Mathematica for purpose of testing, or for exploratory studies of methods that make use of pfaffians.
Program title:Pfaffian
Catalogue identifier: AEJD_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJD_v1_0.html
Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 2281
No. of bytes in distributed program, including test data, etc.: 13 226
Distribution format: tar.gz
Programming language: Fortran 77 and 90
Computer: Any supporting a FORTRAN compiler
Operating system: Any supporting a FORTRAN compiler
RAM: a few MB
Classification: 4.8
Nature of problem: Evaluation of the pfaffian of a skew symmetric matrix. Evaluation of pfaffians arises in a number of physics applications involving fermionic mean field wave functions and their overlaps.
Solution method: Householder tridiagonalization. Aitkenʼs block diagonalization formula.
Additional comments: Python and Mathematica implementations are provided in the main body of the paper.
Running time: Depends on the size of the matrices. For matrices with 100 rows and columns a few milliseconds are required.
► Numeric and symbolic evaluation of pfaffian. ► Cholewsky like decomposition of skew-symmetric matrix.
We argue that macroscopic electrodynamics is unsuited to describe the process of radiative thermalization between a levitated nanoparticle in high vacuum and the thermal electromagnetic field. Based ...on physical arguments, we propose a model to describe such systems beyond the quasiequilibrium approximation. We use path integral techniques to analytically solve the model and exactly calculate the time evolution of the quantum degrees of freedom of the system. Free parameters of the microscopic quantum model are determined by matching analytical results to well-known macroscopic response functions. The time evolution of the internal energy of a levitated nanoparticle in a thermal electromagnetic field, as described by our model, qualitatively differs from macroscopic electrodynamics, a prediction that can be experimentally tested.
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