Quantum NanoOptomechanics and Forces (QNOF)

The QNOF group shares experience with the NEMS group in Aalto University in microwave optomechanics and on the nanofabrication techniques of microscopic suspended superconducting membranes coupled to cavity resonators. In the NEMS group led by Pr. Mika Sillanpää, multimode optomechanical systems were used to build devices relevant for quantum technology (amplifiers, nonreciprocal systems such as directional amplifiers or isolators [1][2]), to investigate complex mechanical coupling situations and their impact on the thermodynamics of mechanical oscillators [3], to develop sensitive displacement detection methods [4] adapted for quantum states measurements and demonstrate steady-state mechanical entanglement [5][6].

Part of the QNOF group's interest is to continue this line of research in close collaboration with the NEMS group (although both groups investigate different topics). Currently, the QNOF group is studying the possibilities offered by gated optomechanics in modulating the parameters of an optomechanical system in time domain [7].

Furthermore, while microwave optomechanical systems, and drum-based systems in particular, have proven their value in a number of breakthroughs in the recent years, they lack a sensitivity to mechanical modes' shape as compared to their optical-domain counterpart. Indeed, microwave wavelengths (centimetric) are typically larger than mechanical oscillators (10 μm - 1 mm,  for those that can be reasonably well coupled to electromagnetic fields), while optical wavelengths (100 nm - 1 μm) are smaller, so that it is possible to focus light on small portions of oscillators. Another current objective of the QNOF group is to integrate microwave optomechanical systems with an optical scanning device (in a dilution cryostat) to grant the system a spatial resolution. This will allow to combine the large optomechanical couplings offered by microwave optomechanics and the possibility to map out mechanical modes, to realize ultra-sensitive force measurements.

_{[1] L. Mercier de Lépinay, E. Damskägg, C. F. Ockeloen-Korppi and M. A. Sillanpää, Phys. Rev. Appl. 11, 34027 (2019)  [arXiv]}

_{[2] L. Mercier de Lépinay, C. F. Ockeloen-Korppi, D. Malz, and M. A. Sillanpää, Phys. Rev. Lett. 125(2), 23603 (2020)  [arXiv]}

_{[3] L. Mercier de Lépinay, C. F. Ockeloen-Korppi, D. Malz, C. Wanjura, A. Nunnenkamp, and M. A. Sillanpää, in preparation}

_{[4] C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, A. A. Clerk, M. J. Woolley, and M. A. Sillanpää, Phys. Rev. Lett. 117, 140401 (2016) [arXiv]}

_{[5] C. F. Ockeloen-Korppi, E. Damskägg, J. M. Pirkkalainen, M. Asjad, A. A. Clerk, F. Massel, M. J. Woolley and M. A. Sillanpää, Nature, 556, 478–482 (2018)  [arXiv]}

_{[6] L. Mercier de Lépinay, C. F. Ockeloen-Korppi, M. J. Woolley, and M. A. Sillanpää, Science (New York, N.Y.), 372 (6542), 625–629 (2021)  [arXiv]}

_{[7] R. W. Andrews,  A. P. Reed, K. Cicak, J. D. Teufel, and K. W. Lehnert, Nat. Commun. 6, 10021 (2015)  [arXiv]}

The Casimir force [1] is an attraction between closely spaced surfaces that can be seen either as an effect of the radiation pressure of quantum fluctuations of the electromagnetic field, or as an effect of the retarded response of electrons of one surface to the relativistic motion of electrons in the other. A current objective of the QNOF group is to realize the measurement of the Casimir force between superconductors.

Even though the Casimir force was already predicted in the 1950s [1] and has been well observed since then [2][3], some aspects of this phenomenon remain very mysterious. All electromagnetic frequencies of the spectrum contribute to the force, and especially the higher frequencies, but the contribution of the lower-frequency part of the spectrum is not fully understood.

Thermal contribution to the Casimir force

There also exists a thermal contribution to the Casimir force, but it remains somewhat mysterious to this day [4][5]. Using well tested models of optical responses (the Drude model) to compute estimates of this contribution results in counter-intuitive predictions. On the other hand, the plasma model, that fails to reproduce the low-frequency response of metals, seems to match most measurement results and produces less counter-intuitive predictions for the thermal Casimir force. Therefore, there remains a puzzle around the contribution of low-frequencies to the Casimir force, and in particular to its thermal contribution.

Using the superconducting gap as a filter

Interestingly, the optical response of superconductors is different from normal metals' only for low frequencies, below the superconducting gap [6]. Therefore, the Casimir force difference across the superconducting transition is only contributed by low optical frequencies. The superconducting gap can therefore be used as a filter for low frequencies to investigate the contribution to the force of the problematic part of the spectrum [7][8].

Furthermore, operating in dilution refrigerators allows to vary the temperature over 2 orders of magnitude (10 mK- 1K) below the transition temperature, and therefore vary the magnitude of the thermal correction to the Casimir force significantly.

Casimir force measurement with drum resonators

Drum resonators are made of very parallel plates and compliant with sensitive microwave optomechanical measurement of force. The QNOF group is therefore aiming at measuring the Casimir force between the two plates of aluminum drum resonators, and more specifically the difference of Casimir force across the superconducting transition.

Thanks to the large panel of equipment available on site, it will also be possible to characterize surface microscopic details (patch potentials) and make statistical models of their impact on force measurement. Coupling the cryogenic microwave optomechanical setup with an optical interferometer (see below) will allow to measure the drum's vacuum gap in situ.

_{[1] H. B. G. Casimir,  Proc. K. Ned. Akad. Wetensch. Proc. 51, 793 (1948)}  

_{[2] R. S. Decca, D. López, E. Fischbach, G. L. Klimchitskaya, D. E. Krause, and V. M Mostepanenko, Phys. Rev. D 75, 77101 (2007)  [arXiv]}

_{[3] S. K. Lamoreaux, Phys. Rev. Lett. 78, 5-8 (1997)}

_{[4] A. O. Sushkov, , W. J. Kim, D. A. R. Dalvit, S. K. Lamoreaux, Observation of the thermal Casimir force. Nat. Phys. 7, 230-233 (2011)  [arXiv]}

_{[5] V. M. Mostepanenko, V. B. Bezerra, R. S. Decca, B. Geyer, E. Fischbach, G. L. Klimchitskaya, D. E. Krause, D. López, and C. Romero, Journal of Physics A, 39, 6589-6600 (2006)  [arXiv]}

_{[6] G. Bimonte, H. Haakh, C. Henkel, and F. Intravaia, Journal of Physics A 43, 145304 (2010)  [arXiv]}

_{[7] G. Bimonte, Phys. Rev. A 78, 62101 (2008)  [arXiv]}

_{[8] G. Bimonte, Phys. Rev. A 99, 52507 (2019)  [arXiv]}

Operation at cryogenic temperatures (dilution refrigerator temperatures, 10 mK - 100 mK) is the most efficient way to maintain mechanical oscillators in a low thermal vibration state and therefore cut the main source of noise in force measurement. This comes with other advantages: mechanical quality factors are higher than at room temperature, and a number of metals turn superconducting, allowing for very low loss electromechanical detection of motion. However, because of the Meissner effect repelling magnetic flux lines from superconductors (or restricting flux threading superconducting materials to quantized values) superconducting mechanical oscillators are likely to be subject to additional forces in presence of a magnetic field. Indeed, the deformation of the superconductor entails a deformation of flux lines and therefore a variation of the energy cost of the flux lines bending.

To study this mechanical impact, it is important to map out the magnetic state of superconducting oscillators in situ. Magnetic imaging is possible with SQUID scanning devices or using magneto-optically active materials (Faraday rotators, in a Kerr microscope configuration). SQUID imaging is well adapted to very low temperatures, but does not allow for fast imaging. On the other hand, magneto-imaging techniques, which can allow very fast imaging [1], might become difficult to implement at extremely low temperatures as indicator materials might go through phase transitions suppressing their magneto-optic sensitivity.

We are working to building an ultra-low temperature Kerr microscope using ultra-strong Faraday materials grown locally by epitaxy. The microscope could help understand the impact of vorticity on superconducting structures, mechanical or not, and complement the rather sparse knowledge of vortex state in aluminum-based quantum technologies [2]. This optical microscope could then be coupled with vortex manipulation capabilities as has been realized at higher temperatures in LOMA in Bordeaux [1][3] to investigate the interaction between mechanical oscillators and quantized flux in superconductors.

_{[1] I. S. Veshchunov, W. Magrini, S. V. Mironov, A. G. Godin, J.-B. Trebbia, A. I. Buzdin, Ph. Tamarat, and B. Lounis, Nat. Commun. 7 12801 (2016) [arXiv]}

_{[2] C. Song, T. W. Heitmann, M. P. DeFeo, K. Yu, R. McDermott, M. Neeley, J. M. Martinis, and B. L. T. Plourde, Phys. Rev. B 79, 174512 (2009)  [arXiv]}

_{[3] A. Rochet, V. Vadimov,  W. Magrini, S. Thakur, J.-B. Trebbia, A. Melnikov, A. Buzdin, Ph. Tamarat, and B. Lounis, Nano Letters 20, 6488-6493 (2020)}

The group is carrying out experiments using microwave and RF engineering techniques, cryogenic techniques (in dilution cryostats, temperatures down to some 10 mK), and optics (in development). Shared resources are occasionally used, and the group is currently getting equipped with a state-of-the-art dry dilution cryostat.

Samples (drum resonators, microwave resonators, small filters...) are nanofabricated and characterized within the group using two cleanrooms:

• the Nanotalo cleanroom with a series of readily available, self-maintained common instruments,
• the Micronova cleanroom with a very large and rich set of instruments with redundancies to reduce the impact of instrument downtime.

The Department of Applied Physics and the OtaNano infrastructure offer a large panel of experimental equipment available on site, as well as from the experience and skills to maintain this equipment and guide users.