WP10: Collective quantum excitations as quantum sensors (involving the University of Exeter, Imperial College London, University of Oxford, University of Nottingham, University of Strathclyde and University of Sussex)

<<Under construction>>

Quantum sensing, including the measurements of the local gravitational field and the detection of dark energy, is usually performed using interferometric techniques. These techniques involve quantum systems in spatial superpositions. Here, the sensitivity improves with the number of systems and with T^2, where T is the time of flight. In atom interferometry, the atom-atom interactions are negligible and the sensitivity is limited by the available time of flight, which requires large spatial separations or long interferometer arms. Therefore, such detectors cannot be miniaturized without loss in sensitivity.

An alternative is to use the collective excitations (phonons) of atomic systems as the quantum sensors. This enables interference in the frequency domain, i.e. between modes that are sharp in frequency and delocalized over the whole extension of the system (approximately one millimeter). An advantage of this is that detectors can be miniaturized using in-chip technology. The atom-atom interactions act as Hamiltonian non-linearities producing two-mode squeezing between pairs of frequency modes when the system size undergoes periodic oscillations. Members of our team have shown that these interactions are very sensitive to periodic spacetime changes when the phonons have been prepared in squeezed states (which entails that the atoms have been entangled). For example, an oscillating gravitational field will cause an interacting atomic system to vibrate, increasing phonon numbers through parametric amplification. In low temperature systems, such as Bose-Einstein condensates (BECs), these changes can be in principle observed through state-of-the-art measurement techniques.

Quantum resonances enhance the effects when the sum or difference of two squeezed phononic modes equals the frequency of the spacetime perturbation. Therefore, this proposed sensor can be thought of as a quantum version of a Weber bar, where temperatures in the nK regime enable vibrational modes to exhibit quantum behaviour. One can then exploit quantum properties such as entanglement and squeezing, and apply quantum metrology and sensing techniques to reach extremely high sensitivities. These techniques have led to proposals for using collective excitations to measure the gravitational field of a small mass, enabling, for example: precision measurements of the gravitational constant [1]; proposals for further constraining fifth forces and dark energy models in the form of screened scalar fields [2]; proposals for on-chip gravimetry and gradiometery; and measurements of gravitational waves in the kHz and GHz regime [3]; At these frequencies interesting signals appear, such as those generated from cosmic strings, primordial black holes, and dark matter, which would all provide deep insights into the workings of our universe.

Quantum Weber Bar

Since our proposed detector is a resonator, it resembles a Weber bar, which was the first kind of gravitational wave detector to be built. The vibrational modes of a Weber bar are in resonance with gravitational waves, but this is a regular resonance rather than a parametric one, and the vibrational modes are in the classical regime. Weber bars did not succeed at detecting gravitational waves because they were too hot (some cooled down to 5K). However, BECs are the coldest objects that we know of, reaching temperatures as low as 5x10^-10 K. The speed of sound c_s in a Weber bar is 1 km/s and their lengths L are of order 1m. Since phononic mode frequencies are given by n=nc_s/L, gravitational waves with frequencies of order 1 kHz can, in principle, be detected in these systems.  In a BEC, the speed of sound is around 10 mm/s and lengths vary from 10^-6 - 10^-3 m. This coincidentally also allows for detection of gravitational waves in the kHz regime, but now with much smaller systems.  If instead we consider an electromagnetic cavity (with no dielectric) then for photons to be in resonance with the gravitational waves of frequency 1 Hz - 100 KHz, we would need cavity sizes of order 10⁸-10³ m, with the dimensions of LIGO coincidently being about 10³ m.

The main difference between a Weber bar and our proposal is that at the low temperatures reached in condensation, the phononic excitations are in the quantum regime. This enables us to exploit quantum properties such as entanglement and squeezing, which are well-known to make parameter estimation far more sensitive than with classical methods. In that sense, our proposed detector can be seen as a quantum version of a Weber bar.

[1] D. Rätzel, R. Howl, J. Lindkvist and I. Fuentes, New J. Phys. 20, 073044 (2018).

[2] D. Hartley, C. Käding, R. Howl and I. Fuentes, in preparation

[3] C. Sabín, D. E. Bruschi, M. Ahmadi, and I. Fuentes, New Journal of Physics 16, 085003 (2014); C. Sabín, J. Kohlrus, D. E. Bruschi, and I. Fuentes, EPJ Quantum Technology 3, 8 (2016).

 

Participants

• Gerardo Adesso (University of Nottingham)
• Aidan Arnold (University of Strathclyde)
• Philippe Bouyer (CNRS, France)
• Clare Burrage (University of Nottingham)
• Luis A. Correa (University of Exeter)
• Jo Cotter (Imperial College London)
• Thomas Fernholz (University of Nottingham)
• Ivette Fuentes (University of Nottingham)
• Barry Garraway (University of Sussex)
• Daniel Goldwater (University of Nottingham)
• Paul Griffin (University of Strathclyde)
• Richard Howl (University of Nottingham)
• Paul Knott (University of Nottingham)
• Peter Krüger (University of Sussex)
• John March-Russell (University of Oxford)
• Devang Naik (CNRS, France)
• Fedja Orucevic (University of Sussex)
• Roger Penrose (University of Oxford)
• German Sinuco (University of Sussex)
• Christopher Westbrook (CNRS, France)

Contacts

 Barry Garraway and Ivette Fuentes