Superconducting Quantum Circuits
Group of Gerhard Kirchmair

Coupling mechanical systems to electromagnetic fields and circuits got more and more attention since the question arose in the context of gravitational wave detection in the 1970s. Today, mechanical hybrid systems are omnipresent, e.g. as acceleration sensors in cellphones, cars and more. However, by harnessing quantum effects the sensitivity of these devices can be vastly increased, offering new possibilities for compact ultra-sensitive sensors. Furthermore, micromechanical systems in the quantum regime enable new applications in quantum optics and quantum information, such as highly efficient optical to microwave converters, single photon sources/detectors for microwaves or long lived quantum memory. On a more fundamental aspect, a macroscopic micromechanical system in the quantum regime would also allow investigating open questions concerning the classical to quantum transition and the interplay between gravity and quantum physics.

Our goal is to set up a new type of experiment in which the coupling between mechanics and circuits is achieved inductively, as shown conceptually in Fig.1. This architecture is suited for detecting and cooling the motion of a mechanical oscillator (i.e. cantilever) to the quantum ground state and achieve strong coupling. Ultimately, we aim at reaching the single-photon single-phonon strong coupling regime, where the exchange between a single photon and a single photon can be achieved deterministically. Such a regime would allow for the full quantum control of a macroscopic mechanical object, opening numerous opportunities for technological applications as well as fundamental studies. In a first step towards this goal, we want to detect the motion of the cantilever via magnetic readout using a superconducting quantum interference device (SQUID). Once achieved, we can apply feedback schemes to cool the cantilever and couple it to quantum circuits for exploring the quantum regime.

Strong Quantum Magnetomechanical CouplingStrong Quantum Magnetomechanical Coupling

The zero point motion of mesoscopic mechanical oscillators is typically on the order of a few femtometers. Detecting the ground state therefore requires extremely high sensitivities with a minimal backaction. Unfortunately, optical readout suffers from shot noise and backaction due to photon momentum transfer. In contrast, magnetic readout could evade this backaction by using a SQUID as a sensitive field to voltage converter. In this case, it would require a magnetic signal generated by the cantilever. In the simplest setup, this can be achieved by placing a ferromagnetic strip on the cantilever. While this approach would provide large coupling strength, it is not sufficient to reach the single-photon strong coupling regime.

In [1], we demonstrated theoretically that by using a superconducting strip on the cantilever and a flux dependent quantum circuit, as illustrated in Fig. 1, we could attain the single-photon single-phonon coupling regime. Here instead of a ferromagnetic, an external quadrupolar magnetic field is used to generate sheet currents in the superconducting strip which is maintained in the Meissner state. As a result, the position dependent response of the system, and consequently the coupling strength, is greatly enhanced by both diamagnetism and demagnetizing effects allowing to reach the strong coupling regime.

Fig. 1: Schematic illustration of the proposal. A superconducting strip (red rectangle) is deposited on the tip of the cantilever (orange). A SQUID (red wire) placed above the cantilever collects the flux generated by the currents in the strip induced by an external quadrupole field. The field is generated by two parallel wires with opposite currents (in black) placed below the cantilever.

As a first step towards the experimental realization of the strong magnetomechanical coupling, we are currently characterizing the quadrupolar magnetic field generation, the DC-SQUID readout and the mechanical resonator. In Fig. 2 we show a microchip containing DC SQUID’s, mounted to a circuit board, being used for the characterization of the SQUID readout.
In a second step, the SQUID chip and the chip holding the mechanical oscillator are accurately placed together in a flip-chip configuration and cooled down to below one Kelvin in a dilution cryostat. The following step consists in applying and optimizing an active feedback scheme to cool the cantilever to its groundstate. This is necessary to reach the quantum regime and the starting point for studying quantum mechanical effects in a macroscopic object. Furthermore, upon reaching the strong coupling regime, an important milestone in this field, it will be possible to create non Gaussian mechanical states such as cat states or Fock states.

Fig. 2: Microchip with eight DC-SQUIDs mounted to a printed circuit board for readout.

[1] Strong Single-Photon Coupling in Superconducting Quantum Magnetomechanics
G. Via, G. Kirchmair, and O. Romero-Isart
Phys. Rev. Lett. 114, 143602 (2015)

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