P. F. Barker’s research while affiliated with University College London and other places

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Publications (78)


A diagram illustrating the creation of a spherically symmetric radial optical potential around a nanosphere trapped in a Paul trap. The potential, which is always centred on the nanosphere, is created by both the incident and scattered fields from three loosely focused orthogonally polarized optical fields, shown in blue.
The total near-field intensity normalized by the incident beam intensity in the y–z plane. The light of wavelength 1000 nm is incident on a nanosphere of 40 nm radius with and a refractive index of n = 1.43. The field inside the nanosphere, shown as the circular white region, is not plotted. (a) Is a plot of the intensity when illuminated by a single field propagating in the x direction and polarized in the z direction. (b) A plot of the intensity when illuminated by three orthogonally propagating fields with orthogonal polarizations.
The radial potential formed by the combination of an attractive short range potential due to the C–P force and a short and long range potential formed by a repulsive optical dipole potential using near field light around a nanoparticle of radius 40 nm. The red line is the full potential and the black line is the Yukawa potential approximation with µ = 20 µm. The inset figure is the classical momentum transfer cross-section for metastable helium atoms when the nanosphere is illuminated by light at the magic wavelength of 318.611 nm.
(a) The radial potential formed by the combination of an attractive short-range Casimir–Polder potential and a long range component formed by an attractive and repulsive optical dipole potentials from the scattering of the light from the nanoparticle. (b) Plots of the first four wavefunctions and their energies with respect to this radial potential.
The total scattering cross-section as function of collision energy in units of µK for the potential shown in figure 4. A shape resonance at E = 0.01 µK l = 33 is observed.

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A levitated atom-nanosphere hybrid quantum system
  • Article
  • Full-text available

January 2024

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49 Reads

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1 Citation

A Hopper

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P F Barker

Near-field, radially symmetric optical potentials centred around a levitated nanosphere can be used for sympathetic cooling and for creating a bound nanosphere-atom system analogous to a large molecule. We demonstrate that the long range, Coulomb-like potential produced by a single blue detuned field increases the collisional cross-section by eight orders of magnitude, allowing fast sympathetic cooling of a trapped nanosphere to microKelvin temperatures using cold atoms. By using two optical fields to create a combination of repulsive and attractive potentials, we demonstrate that a cold atom can be bound to a nanosphere creating a new levitated hybrid quantum system suitable for exploring quantum mechanics with massive particles.

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Optimal Superpositions for Particle Detection via Quantum Phase

July 2023

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34 Reads

Exploiting quantum mechanics for sensing offers unprecedented possibilities. State of the art proposals for novel quantum sensors often rely on the creation of large superpositions and generally detect a field. However, what is the optimal superposition size for detecting an incident particle (or an incident stream of particles) from a specific direction? This question is nontrivial as, in general, this incident particle will scatter off with varied momenta, imparting varied recoils to the sensor, resulting in decoherence rather than a well defined measurable phase. By considering scattering interactions of directional particulate environments with a system in a quantum superposition, we find that there is an "optimal superposition" size for measuring incoming particles via a relative phase. As a consequence of the anisotropy of the environment, we observe a novel feature in the limiting behaviour of the real and imaginary parts of the system's density matrix, linking the optimality of the superposition size to the wavelength of the scatterer.


FIG. 1. (a) The experimental setup for sympathetic cooling and squeezing. Two 387-nm-diameter, silica particles are trap simultaneously in a Paul trap. One arm of a 637-nm laser is focused onto each particle individually. The power in each arm is balanced such that the scattering from each particle is approximately equal when measured on the CMOS camera. One of the arms is also focused onto a quadrant photodiode for real-time detection of the motion of one particle. A force is applied to the same particle to either cool or squeeze the normal modes by modulating the power of a 1030-nm laser. The feedback signal is generated from the real-time measurement of the particle position. BS: beam splitter, QP: quadrant photodiode, and SPF: short-pass filter. (b) Two cotrapped particles in the Paul trap. The separation between these particles is 198 ± 1 μm.
FIG. 3. (a) Spectra for the cooled z + (left) and z − (right) modes at a pressure of P = 3.2 × 10 −7 mbar (dark lines) shown alongside the spectra of the modes with no cooling at P = 1.3 × 10 −2 mbar (light lines) where the modes are expected to be in thermal equilibrium with the surrounding gas. (b) Temperature of the normal modes in the experiment (markers) and theory (lines) vs feedback gain. The disagreement between theory and experiment suggests there is an additional source of heating for the normal modes.
FIG. 4. Phase-space diagrams showing a thermal and squeezed state for the z + mode of both particles at a pressure of P = 1.2 × 10 −2 mbar. Both particles display squeezed states despite interaction with only particle 1. The particles used here have approximately equal charges; therefore the mode energies should be equal as they appear here.
Sympathetic cooling and squeezing of two colevitated nanoparticles

January 2023

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109 Reads

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40 Citations

Physical Review Research

Levitated particles are an ideal tool for measuring weak forces and investigating quantum mechanics in macroscopic objects. Arrays of two or more of these particles have been suggested for improving force sensitivity and entangling macroscopic objects. In this article, two charged, silica nanoparticles, that are coupled through their mutual Coulomb repulsion, are trapped in a Paul trap, and the individual masses and charges of both particles are characterized. We demonstrate sympathetic cooling of one nanoparticle coupled via the Coulomb interaction to the second nanoparticle to which feedback cooling is directly applied. We also implement sympathetic squeezing through a similar process showing nonthermal motional states can be transferred by the Coulomb interaction. This work establishes protocols to cool and manipulate arrays of nanoparticles for sensing and minimizing the effect of optical heating in future experiments.


Measurement of the motional heating of a levitated nanoparticle by thermal light

January 2023

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9 Reads

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1 Citation

Physical Review A

We report on measurements of the photon-induced heating of silica nanospheres levitated in a vacuum by a thermal light source formed by a superluminescent diode. Heating of the nanospheres motion along the three trap axes was measured as a function of gas pressure for two particle sizes and recoil heating was shown to dominate other heating mechanisms due to relative intensity noise and beam pointing fluctuations. Heating rates were also compared with the much lower reheating of the same sphere when levitated by a laser.


FIG. 1. (a) Inset illustrates a nanoparticle, trapped by an optical tweezer with x-y mechanical modes. The presence of a surrounding cavity, required for quantum cooling, hybridizes the modes and shifts their unperturbed frequencies ω (0) x,y . The experimental tweezer polarization sets an initial angle θ between the x-y modes and cavity axis. Then, the optomechanical cavity hybridization dynamics adds an effective mode rotation dyn . However, away from optical nodes, the CS field opposes this effect. (b) We investigate mode orientation by measuring cross-correlation spectra S xy (ω) for θ π/4 as the trapping position is swept from node (blue, φ = π/2) to near the antinode (red, φ = 0) of the cavity standing wave. The x-y motions are always anticorrelated (peaks of opposite sign), but S xy flips sign at φ = φ c [purple line, S xy (ω) ∼ 0]. For this value, the CS field cancels dyn : the mechanical modes are locked at their unperturbed orientations and unperturbed frequencies for arbitrary power and θ, but can still be strongly cooled. The results have implications for directional force sensing and, in strong coupling regimes, the suppression of dark/bright modes.
FIG. 3. (a) To measure mode rotation, we compare crosscorrelation spectra S xy (ω) with the rescaled difference between PSDs S xy (ω) (φ) [S yy (ω) − S xx (ω)] to extract (φ). Plots show experimental S xy at a node, /2π = −360 kHz and rescaled, measured, S yy − S xx . The rescaling gives excellent agreement, but there is a bias β ≈ 0.03 arising from an imperfection in the orientation of the D mirror (∼2 • ) for the x detector. This yields a systematic shift between the scaling of all points obtained from the y peak (lower frequency) and the x peak (higher frequency). In Fig. 2, all y (cyan) data points are shifted by a constant, (φ) → (φ) − β . Upper red curve shows x-y hybridization mediated by the cavity mode. (b) Illustrates the "locking" of the mode orientation at φ = φ c . (i) (Top) For /2π = −176 kHz, nearing resonance at ω x,y /(2π ) ∼ 150 kHz, φ c /2π = 0.145. At this point, for arbitrary tweezer polarization θ or input power, the modes remain at the unperturbed orientations. (ii) (Bottom) For large detuning −/2π > 350 kHz, the locking point is φ c /2π = 0.125. For lower detunings, φ c moves towards the node and at /2π = −150 kHz, φ c /2π 0.15.
FIG. 4. (a) 3D schematic overview of the experimental setup highlighting the orientation of the tweezer and cavity field. (b) Optical layout of the split detection.
FIG. 6. Density plot of the cancellation point φ c = tan −1 ( C φ ) as a function of the cavity linewidth κ and optical detuning , with black contours at notable values. C φ is shown in Eq. (D3). Whitedashed lines show the experimental parameters, with white dots representing the two sets of data taken where φ c was investigated. As highlighted by Fig. 2 in the main text, the φ c predictions agree well with experimental observations. The blank ellipse in the top left is the case where C φ < 0, leading to complex-valued φ c that is not plotted. This condition leads to 2 + κ 2 /4 < ω 2 y , showing the ellipse's radii to be 2ω y and ω y in the κ and axes, respectively. The large detuning limit of φ c /2π → 0.125 can be seen in the lower half. The plot suggests that experiments with this cavity (κ = 396 kHz · 2π 2.9 ω y ) are limited to φ c /2π ∼ 0.17, even in a very small detuning limit − ω y . Nevertheless, the higher-valued (brighter) area around the φ c /2π = 0.2 contour suggests that a better cavity with a realistically lower κ 2ω y , may have cancellation closest to the node with φ c /2π ∼ 0.2, so long as the detuning is below resonance. However, if the detuning is above resonance, the φ c /2π = 0.1 contour highlights a region where an increasingly perfect cavity κ ω y may even move φ c toward the antinode.
FIG. 7. Compares the accuracy of the suppression of at the node (top panels) relative to the cancellation point φ c . At the cancellation point, a small frequency dependent residue remains. (a) /2π = −176 kHz (left). At φ c = 0.145, the mode rotation is suppressed by a factor ≈ 100 relative to the node (right) /2π = −176 kHz; at φ c = 0.126 the mode rotation is suppressed by a factor ≈ 250 relative to the node . (b) /2π = −136 kHz, finesse increased by a factor 1.5 relative to experiments. Now φ c = 0.17 is significantly closer to the node, but the residue is larger and suppression is only by one order of magnitude. Black lines are cross-correlation spectra, green are the rescaled difference spectra ((S yy − S xx ). Note that the small residue at the cancellation points does not in general follow the rescaled PSDs.
Controlling mode orientations and frequencies in levitated cavity optomechanics

January 2023

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65 Reads

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7 Citations

Physical Review Research

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H. Fu

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T. S. Monteiro

Cavity optomechanics offers quantum ground state cooling, control and measurement of small mechanical oscillators. However optomechanical backactions disturb the oscillator motions: they shift mechanical frequencies and, for a levitated oscillator, rotate the spatial orientation of the mechanical modes. This introduces added imprecisions when sensing the orientation of an external force. For a nanoparticle trapped in a tweezer in a cavity populated only by coherently scattered (CS) photons, we investigate experimentally mode orientation, via the Sxy(ω) mechanical cross-correlation spectra, as a function of the nanoparticle position in the cavity standing wave. We show that the CS field rotates the mechanical modes in the opposite direction to the cavity backaction, canceling the effect of the latter. It also opposes optical spring effects on the frequencies. We demonstrate a cancellation point, where it becomes possible to lock the modes near their unperturbed orientations and frequencies, independent of key experimental parameters, while retaining strong light-matter couplings that permit ground state cooling. This opens the way to sensing of directionality of very weak external forces, near quantum regimes.


Overview of technologies with a technological readiness level (TRL) <6 . Black semicircles: critical. *: required if the optical bench (OB) is covered. **: required if the OB is open to space.
Timeline of key activities. CS: CubeSat, FM: flight model, op.: operation.
Research campaign: Macroscopic quantum resonators (MAQRO)

January 2023

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286 Reads

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14 Citations

The objective of the proposed MAQRO mission is to harness space for achieving long free-fall times, extreme vacuum, nano-gravity, and cryogenic temperatures to test the foundations of physics in macroscopic quantum experiments at the interface with gravity. Developing the necessary technologies, achieving the required sensitivities and providing the necessary isolation of macroscopic quantum systems from their environment will lay the path for developing novel quantum sensors. Earlier studies showed that the proposal is feasible but that several critical challenges remain, and key technologies need to be developed. Recent scientific and technological developments since the original proposal of MAQRO promise the potential for achieving additional science objectives. The proposed research campaign aims to advance the state of the art and to perform the first macroscopic quantum experiments in space. Experiments on the ground, in micro-gravity, and in space will drive the proposed research campaign during the current decade to enable the implementation of MAQRO within the subsequent decade.


FIG. 1. Schematic representation of an ellipsoidally shaped nanoparticle trapped in an optical tweezer. The three Euler angles (a, b, and c) and three centers of mass coordinates are shown in the convention used throughout the work (laboratory frames: x, y, and z; body frames: x 00 ; y 00 , and z 00 ).
Measurement of single nanoparticle anisotropy by laser induced optical alignment and Rayleigh scattering for determining particle morphology

November 2022

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117 Reads

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12 Citations

We demonstrate the measurement of nanoparticle anisotropy by angularly resolved Rayleigh scattering of single optical levitated particles that are oriented in space via the trapping light in vacuum. This technique is applied to a range of particle geometries from perfect spherical nanodroplets to octahedral nanocrystals. We show that this method can resolve shape differences down to a few nanometers and be applied in both low-damping environments, as demonstrated here, and in traditional overdamped fluids used in optical tweezers.




Cavity optomechanics in a fiber cavity: the role of stimulated Brillouin scattering

September 2022

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86 Reads

We study the role of stimulated Brillouin scattering in a fiber cavity by numerical simulations and a simple theoretical model and find good agreement between experiment, simulation and theory. We also investigate an optomechanical system based on a fiber cavity in the presence on the nonlinear Brillouin scattering. Using simulation and theory, we show that this hybrid optomechanical system increases optomechanical damping for low mechanical resonance frequencies in the unresolved sideband regime. Furthermore, optimal damping occurs for blue detuning in stark contrast to standard optomechanics. We investigate whether this hybrid optomechanical system is capable cooling a mechanical oscillator to the quantum ground state.


Citations (38)


... Examples include quantum superpositions of Minkowski spacetime [22] and the signatures of rotating black holes in quantum superpositions [23]. Researchers are also attempting to apply these concepts to analog black holes [24,25], building on earlier work [26][27][28][29], and testing quantum effects in gravity through tabletop experiments [30][31][32]. Black hole mass superpositions provide a novel approach to studying quantum black holes and advancing the theory of quantum gravity. ...

Reference:

Quantum correlation of Hawking radiations for mass-superposed BTZ black holes
A Spin Entanglement Witness for Quantum Gravity
  • Citing Preprint
  • July 2017

... Our results are particularized for the quadrupolar transition 6S 1/2 − 6D 5/2 of the cesium atom and a nanoantenna made of silver. The motivation for analyzing this simple setup is that it can provide an accessible platform for trapping and manipulating an atom [43,44], as well as for controlling the atomic radiative properties. ...

A levitated atom-nanosphere hybrid quantum system

... Indeed, coupling between two particles has been explored on different platforms including electrodynamic and gravito-optical traps, and optical tweezers. These experiments have demonstrated sympathetic cooling [23][24][25][26] and squeezing [25], cold damping [27], optical binding yielding anti-reciprocal coupling [28] and strong Coulomb coupling [29]. This body of work represents the first building block toward more enticing experiments such as the generation and observation of entanglement between mesoscopic objects [30][31][32], and the exploration of the quantum nature of gravity [33]. ...

Sympathetic cooling and squeezing of two colevitated nanoparticles

Physical Review Research

... [9,10] The decoherence resulting from gas molecule collisions will be smaller than that caused by photon recoil if the residual gas pressure is sufficiently low. [11][12][13] When the optomechanical coupling is larger than the decoherence rate it enables entanglement at a macroscopic scale. [14] Levitated optomechanical systems, capable of optically levitating nano-and micro-objects in an ultra-high vacuum environment, have been behind many recent scientific achievements, including the ground-state cooling of motional modes, [9,[15][16][17] strong and ultra-strong optomechanical coupling, [18][19][20][21] quantum squeezing of the motional mode, [22,23] phonon lasers, [24,25] dipole-dipole interaction between two levitated nanoparticles [26] and ultra-high sensitivity force sensing. ...

Measurement of the motional heating of a levitated nanoparticle by thermal light
  • Citing Article
  • January 2023

Physical Review A

... Another recent experimental study investigated the back-action induced rotation of the particle's normal modes. 81 A particular trapping position where the back-action induced rotation is canceled by an interference with the trapping field 79 was demonstrated. At this point, externally induced correlations are exposed since the misalignment caused by these (parameter-sensitive) mode rotations is eliminated. ...

Controlling mode orientations and frequencies in levitated cavity optomechanics

Physical Review Research

... The calculation of the scattered field relies on the acquisition of the T -matrix of the particle. Therefore, precise characterization of the particle is crucial, including its mass [63][64][65] and anisotropy [66], as well as power spectral analysis [67]. This enables shot-noise-limited detection across all degrees of freedom for larger particles, including Mie particles, and facilitates various applications based on macroscopic quantum states. ...

Measurement of single nanoparticle anisotropy by laser induced optical alignment and Rayleigh scattering for determining particle morphology

... In the future, we anticipate that the performance of our experimental set-up could be considerably enhanced in a cryogenic environment [23][24][25][26] . Consequently, this development paves the way for our system to explore a broader spectrum of fundamental physics issues 27 . These include, but are not limited to, the investigation of https://doi.org/10.1038/s41550-024-02465-8 ...

Research campaign: Macroscopic quantum resonators (MAQRO)

... One can embed a spin defect in a crystal, such as a nitrogenvacancy centre (NVC) in a neutral nanodiamond; for a review; see [19]. Then, this spin can be manipulated with external magnetic pulses to create a macroscopic spatial quantum superposition as in a matter-wave interferometer [20][21][22][23][24][25][26][27][28][29][30] Such systems have a wide range of applications in creating quantum sensors [31][32][33][34][35], to test fundamental physics beyond the Standard Model physics [36][37][38][39][40][41], and last but not least, to test the quantum nature of spacetime in a lab [42][43][44], see also [45]. The latter is the most ambitious programme and aims to witness the quantum nature of gravity through entanglement [46,47]. ...

Entanglement based tomography to probe new macroscopic forces

Physical Review D

... Cold damping [47,48] and sympathetic cooling [49] was achieved for pairs of particles. Electromagnetic trapping has made similar advances, with demonstrations of sympathetic cooling between two spheres [50,51] and scalable detection and cooling using cameras [52][53][54] implemented using radio frequency Paul traps. Coulomb interactions between spheres co-trapped in a magnetic potential have also been studied [55]. ...

Imaging-based feedback cooling of a levitated nanoparticle
  • Citing Article
  • July 2022