1
|
Werneck LR, Jessup C, Brandenberger A, Knowles T, Lewandowski CW, Nolan M, Sible K, Etienne ZB, D'Urso B. Cross-correlation image analysis for real-time single particle tracking. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2024; 95:073708. [PMID: 39012180 DOI: 10.1063/5.0206405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2024] [Accepted: 06/25/2024] [Indexed: 07/17/2024]
Abstract
Accurately measuring the translations of objects between images is essential in many fields, including biology, medicine, chemistry, and physics. One important application is tracking one or more particles by measuring their apparent displacements in a series of images. Popular methods, such as the center of mass, often require idealized scenarios to reach the shot noise limit of particle tracking and, therefore, are not generally applicable to multiple image types. More general methods, such as maximum likelihood estimation, reliably approach the shot noise limit, but are too computationally intense for use in real-time applications. These limitations are significant, as real-time, shot-noise-limited particle tracking is of paramount importance for feedback control systems. To fill this gap, we introduce a new cross-correlation-based algorithm that approaches shot-noise-limited displacement detection and a graphics processing unit-based implementation for real-time image analysis of a single particle.
Collapse
Affiliation(s)
- L R Werneck
- Department of Physics, University of Idaho, Moscow, Idaho 83843, USA
| | - C Jessup
- Department of Physics, Montana State University, Bozeman, Montana 59717, USA
| | - A Brandenberger
- Department of Physics, Montana State University, Bozeman, Montana 59717, USA
| | - T Knowles
- Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506, USA
| | - C W Lewandowski
- Department of Physics, Montana State University, Bozeman, Montana 59717, USA
- Space Dynamics Laboratory, Albuquerque, New Mexico 87106, USA
| | - M Nolan
- Department of Physics, Montana State University, Bozeman, Montana 59717, USA
| | - K Sible
- Department of Physics and Astronomy, West Virginia University, Morgantown, West Virginia 26506, USA
- Center for Gravitational Waves and Cosmology, Chestnut Ridge Research Building, Morgantown, West Virginia 26506, USA
- Department of Computer Science and Engineering, University of Notre Dame, South Bend, Indiana 46556, USA
| | - Z B Etienne
- Department of Physics, University of Idaho, Moscow, Idaho 83843, USA
- Department of Physics and Astronomy, West Virginia University, Morgantown, West Virginia 26506, USA
- Center for Gravitational Waves and Cosmology, Chestnut Ridge Research Building, Morgantown, West Virginia 26506, USA
| | - B D'Urso
- Department of Physics, Montana State University, Bozeman, Montana 59717, USA
| |
Collapse
|
2
|
Li X, Cao Y, Ng J. Non-Hermitian non-equipartition theory for trapped particles. Nat Commun 2024; 15:1963. [PMID: 38438361 PMCID: PMC10912716 DOI: 10.1038/s41467-024-46058-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Accepted: 02/13/2024] [Indexed: 03/06/2024] Open
Abstract
The equipartition theorem is an elegant cornerstone theory of thermal and statistical physics. However, it fails to address some contemporary problems, such as those associated with optical and acoustic trapping, due to the non-Hermitian nature of the external wave-induced force. We use stochastic calculus to solve the Langevin equation and thereby analytically generalize the equipartition theorem to a theory that we denote the non-Hermitian non-equipartition theory. We use the non-Hermitian non-equipartition theory to calculate the relevant statistics, which reveal that the averaged kinetic and potential energies are no longer equal to kBT/2 and are not equipartitioned. As examples, we apply non-Hermitian non-equipartition theory to derive the connection between the non-Hermitian trapping force and particle statistics, whereby measurement of the latter can determine the former. Furthermore, we apply a non-Hermitian force to convert a saddle potential into a stable potential, leading to a different type of stable state.
Collapse
Affiliation(s)
- Xiao Li
- Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China
| | - Yongyin Cao
- Institute of Advanced Photonics, School of Physics, Harbin Institute of Technology, Harbin, 150001, China
| | - Jack Ng
- Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China.
| |
Collapse
|
3
|
Brzobohatý O, Duchaň M, Jákl P, Ježek J, Šiler M, Zemánek P, Simpson SH. Synchronization of spin-driven limit cycle oscillators optically levitated in vacuum. Nat Commun 2023; 14:5441. [PMID: 37673926 PMCID: PMC10482900 DOI: 10.1038/s41467-023-41129-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Accepted: 08/23/2023] [Indexed: 09/08/2023] Open
Abstract
We explore, experimentally and theoretically, the emergence of coherent coupled oscillations and synchronization between a pair of non-Hermitian, stochastic, opto-mechanical oscillators, levitated in vacuum. Each oscillator consists of a polystyrene microsphere trapped in a circularly polarized, counter-propagating Gaussian laser beam. Non-conservative, azimuthal forces, deriving from inhomogeneous optical spin, push the micro-particles out of thermodynamic equilibrium. For modest optical powers each particle shows a tendency towards orbital circulation. Initially, their stochastic motion is weakly correlated. As the power is increased, the tendency towards orbital circulation strengthens and the motion of the particles becomes highly correlated. Eventually, centripetal forces overcome optical gradient forces and the oscillators undergo a collective Hopf bifurcation. For laser powers exceeding this threshold, a pair of limit cycles appear, which synchronize due to weak optical and hydrodynamic interactions. In principle, arrays of such Non-Hermitian elements can be arranged, paving the way for opto-mechanical topological materials or, possibly, classical time crystals. In addition, the preparation of synchronized states in levitated optomechanics could lead to new and robust sensors or alternative routes to the entanglement of macroscopic objects.
Collapse
Affiliation(s)
- Oto Brzobohatý
- The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, 612 64, Brno, Czech Republic.
| | - Martin Duchaň
- The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, 612 64, Brno, Czech Republic
| | - Petr Jákl
- The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, 612 64, Brno, Czech Republic
| | - Jan Ježek
- The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, 612 64, Brno, Czech Republic
| | - Martin Šiler
- The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, 612 64, Brno, Czech Republic
| | - Pavel Zemánek
- The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, 612 64, Brno, Czech Republic
| | - Stephen H Simpson
- The Czech Academy of Sciences, Institute of Scientific Instruments, Královopolská 147, 612 64, Brno, Czech Republic.
| |
Collapse
|
4
|
Zielińska JA, van der Laan F, Norrman A, Rimlinger M, Reimann R, Novotny L, Frimmer M. Controlling Optomechanical Libration with the Degree of Polarization. PHYSICAL REVIEW LETTERS 2023; 130:203603. [PMID: 37267539 DOI: 10.1103/physrevlett.130.203603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Revised: 03/07/2023] [Accepted: 04/04/2023] [Indexed: 06/04/2023]
Abstract
Control of the potential energy and free evolution lie at the heart of levitodynamics as key requirements for sensing, wave function expansion, and mechanical squeezing protocols. Here, we experimentally demonstrate versatile control over the optical potential governing the libration motion of a levitated anisotropic nanoparticle. This control is achieved by introducing the degree of polarization as a new tool for rotational levitodynamics. We demonstrate thermally driven free rotation of a levitated anisotropic scatterer around its short axis and we use the rotational degrees of freedom to probe the local spin of a strongly focused laser beam.
Collapse
Affiliation(s)
- J A Zielińska
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - F van der Laan
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - A Norrman
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
- Center for Photonics Sciences, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
| | - M Rimlinger
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - R Reimann
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
- Quantum Research Center, Technology Innovation Institute, Abu Dhabi, United Arab Emirates
| | - L Novotny
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - M Frimmer
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| |
Collapse
|
5
|
Non-Hermitian physics for optical manipulation uncovers inherent instability of large clusters. Nat Commun 2021; 12:6597. [PMID: 34782596 PMCID: PMC8593170 DOI: 10.1038/s41467-021-26732-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2021] [Accepted: 10/18/2021] [Indexed: 11/29/2022] Open
Abstract
Intense light traps and binds small particles, offering unique control to the microscopic world. With incoming illumination and radiative losses, optical forces are inherently nonconservative, thus non-Hermitian. Contrary to conventional systems, the operator governing time evolution is real and asymmetric (i.e., non-Hermitian), which inevitably yield complex eigenvalues when driven beyond the exceptional points, where light pumps in energy that eventually "melts" the light-bound structures. Surprisingly, unstable complex eigenvalues are prevalent for clusters with ~10 or more particles, and in the many-particle limit, their presence is inevitable. As such, optical forces alone fail to bind a large cluster. Our conclusion does not contradict with the observation of large optically-bound cluster in a fluid, where the ambient damping can take away the excess energy and restore the stability. The non-Hermitian theory overturns the understanding of optical trapping and binding, and unveils the critical role played by non-Hermiticity and exceptional points, paving the way for large-scale manipulation.
Collapse
|
6
|
Li X, Zheng H, Yuen CH, Du J, Chen J, Lin Z, Ng J. Quantitative study of conservative gradient force and non-conservative scattering force exerted on a spherical particle in optical tweezers. OPTICS EXPRESS 2021; 29:25377-25387. [PMID: 34614870 DOI: 10.1364/oe.434208] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 07/14/2021] [Indexed: 06/13/2023]
Abstract
We rigorously calculate the conservative gradient force (GF) and the non-conservative scattering force (SF) associated with the optical tweezers (the single beam optical trap). A wide range of parameters are considered, with particle size ranging from the Rayleigh to Mie regime (radius ∼3 µm), dielectric constant ranging from metallic (large and negative) to high dielectrics (large and positive), numerical aperture (NA) ranging from 0.5 to 1.33, and different polarizations. The trap depth associated with GF can reach 123 and 168 kBT per mW for a 0.5 µm-radius polystyrene particle illuminated by a 1064 nm Gaussian beam with NA = 0.9 and 1.3, respectively. This indicates that unless at a low beam power or with a small NA, the Brownian fluctuations do not play a role in the stability. The transverse GF orthogonal to beam propagation always dominates over the transverse SF. While the longitudinal SF can be larger than the longitudinal GF when the scattering is strong, the NA is small, or when absorption is present, optical trapping under these conditions is difficult. Generally speaking, absorption reduces GF and enhances SF, while increasing a dielectric constant enhances GF slightly but boosts SF significantly owing to stronger scattering. These results verify previous experimental observations and explain why optical tweezers are so robust across such a wide range of conditions. Our quantitative calculations will also provide a guide to future studies.
Collapse
|
7
|
Perdriat M, Pellet-Mary C, Huillery P, Rondin L, Hétet G. Spin-Mechanics with Nitrogen-Vacancy Centers and Trapped Particles. MICROMACHINES 2021; 12:651. [PMID: 34206001 PMCID: PMC8227763 DOI: 10.3390/mi12060651] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Revised: 05/24/2021] [Accepted: 05/26/2021] [Indexed: 12/01/2022]
Abstract
Controlling the motion of macroscopic oscillators in the quantum regime has been the subject of intense research in recent decades. In this direction, opto-mechanical systems, where the motion of micro-objects is strongly coupled with laser light radiation pressure, have had tremendous success. In particular, the motion of levitating objects can be manipulated at the quantum level thanks to their very high isolation from the environment under ultra-low vacuum conditions. To enter the quantum regime, schemes using single long-lived atomic spins, such as the electronic spin of nitrogen-vacancy (NV) centers in diamond, coupled with levitating mechanical oscillators have been proposed. At the single spin level, they offer the formidable prospect of transferring the spins' inherent quantum nature to the oscillators, with foreseeable far-reaching implications in quantum sensing and tests of quantum mechanics. Adding the spin degrees of freedom to the experimentalists' toolbox would enable access to a very rich playground at the crossroads between condensed matter and atomic physics. We review recent experimental work in the field of spin-mechanics that employ the interaction between trapped particles and electronic spins in the solid state and discuss the challenges ahead. Our focus is on the theoretical background close to the current experiments, as well as on the experimental limits, that, once overcome, will enable these systems to unleash their full potential.
Collapse
Affiliation(s)
- Maxime Perdriat
- Laboratoire De Physique de l’École Normale Supérieure, École Normale Supérieure, PSL Research University, CNRS, Sorbonne Université, Université de Paris, 24 rue Lhomond, CEDEX 05, 75231 Paris, France; (M.P.); (C.P.-M.); (P.H.)
| | - Clément Pellet-Mary
- Laboratoire De Physique de l’École Normale Supérieure, École Normale Supérieure, PSL Research University, CNRS, Sorbonne Université, Université de Paris, 24 rue Lhomond, CEDEX 05, 75231 Paris, France; (M.P.); (C.P.-M.); (P.H.)
| | - Paul Huillery
- Laboratoire De Physique de l’École Normale Supérieure, École Normale Supérieure, PSL Research University, CNRS, Sorbonne Université, Université de Paris, 24 rue Lhomond, CEDEX 05, 75231 Paris, France; (M.P.); (C.P.-M.); (P.H.)
| | - Loïc Rondin
- Université Paris-Saclay, CNRS, ENS Paris-Saclay, Centrale-Supélec, LuMIn, 91190 Gif-sur-Yvette, France;
| | - Gabriel Hétet
- Laboratoire De Physique de l’École Normale Supérieure, École Normale Supérieure, PSL Research University, CNRS, Sorbonne Université, Université de Paris, 24 rue Lhomond, CEDEX 05, 75231 Paris, France; (M.P.); (C.P.-M.); (P.H.)
| |
Collapse
|