Mechanical frequency control in inductively coupled electromechanical systems

  1. Thomas Luschmann,
  2. Philip Schmidt,
  3. Frank Deppe,
  4. Achim Marx,
  5. Alvaro Sanchez,
  6. Rudolf Gross,
  7. and Hans Huebl
Nano-electromechanical systems implement the opto-mechanical interaction combining electromagnetic circuits and mechanical elements. We investigate an inductively coupled nano-electromechanical
system, where a superconducting quantum interference device (SQUID) realizes the coupling. We show that the resonance frequency of the mechanically compliant string embedded into the SQUID loop can be controlled in two different ways: (i) the bias magnetic flux applied perpendicular to the SQUID loop, (ii) the magnitude of the in-plane bias magnetic field contributing to the nano-electromechanical coupling. These findings are quantitatively explained by the inductive interaction contributing to the effective spring constant of the mechanical resonator. In addition, we observe a residual field dependent shift of the mechanical resonance frequency, which we attribute to the finite flux pinning of vortices trapped in the magnetic field biased nanostring.

Sideband-resolved resonator electromechanics on the single-photon level based on a nonlinear Josephson inductance

  1. Philip Schmidt,
  2. Mohammad T. Amawi,
  3. Stefan Pogorzalek,
  4. Frank Deppe,
  5. Achim Marx,
  6. Rudolf Gross,
  7. and Hans Huebl
as well as the generation of phononic and photonic quantum states [3-10]."]Electromechanical systems realize this optomechanical interaction in the microwave regime. In this context, capacitive coupling arrangements demonstrated interaction rates of up to 280 Hz [11]. Complementary, early proposals [12-15] and experiments [16,17] suggest that inductive coupling schemes are tunable and have the potential to reach the vacuum strong-coupling regime. Here, we follow the latter approach by integrating a partly suspended superconducting quantum interference device (SQUID) into a microwave resonator. The mechanical displacement translates into a time varying flux in the SQUID loop, thereby providing an inductive electromechanical coupling. We demonstrate a sideband-resolved electromechanical system with a tunable vacuum coupling rate of up to 1.62 kHz, realizing sub-aN Hz-1/2 force sensitivities. Moreover, we study the frequency splitting of the microwave resonator for large mechanical amplitudes confirming the large coupling. The presented inductive coupling scheme shows the high potential of SQUID-based electromechanics for targeting the full wealth of the intrinsically nonlinear optomechanics Hamiltonian.

Ultrawide-range photon number calibration using a hybrid system combining nano-electromechanics and superconducting circuit quantum electrodynamics

  1. Philip Schmidt,
  2. Daniel Schwienbacher,
  3. Matthias Pernpeintner,
  4. Friedrich Wulschner,
  5. Frank Deppe,
  6. Achim Marx,
  7. Rudolf Gross,
  8. and Hans Huebl
We present a hybrid system consisting of a superconducting coplanar waveguide resonator coupled to a nanomechanical string and a transmon qubit acting as nonlinear circuit element.
We perform spectroscopy for both the transmon qubit and the nanomechanical string. Measuring the ac-Stark shift on the transmon qubit as well as the electromechanically induced absorption on the string allows us to determine the average photon number in the microwave resonator in both the low and high power regimes. In this way, we measure photon numbers that are up to nine orders of magnitude apart. We find a quantitative agreement between the calibration of photon numbers in the microwave resonator using the two methods. Our experiments demonstrate the successful combination of superconducting circuit quantum electrodynamics and nano-electromechanics on a single chip.

High cooperativity between a phosphorus donor spin ensemble and a microwave resonator

  1. Christoph W. Zollitsch,
  2. Kai Mueller,
  3. David P. Franke,
  4. Sebastian T. B. Goennenwein,
  5. Martin S. Brandt,
  6. Rudolf Gross,
  7. and Hans Huebl
We investigate the coupling of an ensemble of phosphorus donors in an isotopically purified 28Si host lattice interacting with a superconducting coplanar waveguide resonator. The microwave
transmission spectrum of the resonator shows a normal mode splitting characteristic for high cooperativity. The evaluated collective coupling strength geff is of the same order as the loss rate of the spin system γ, indicating the onset of strong coupling. We develop a statistical model to describe the influence of temperature on the coupling strength from 50mK to 3.5K and find a scaling of the coupling strength with the square root of the number of thermally polarized spins.

Quantum State Engineering with Circuit Electromechanical Three-Body Interactions

  1. Mehdi Abdi,
  2. Matthias Pernpeintner,
  3. Rudolf Gross,
  4. Hans Huebl,
  5. and Michael J. Hartmann
We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical
architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanically oscillate. We show that this system design features a three-mode polariton–mechanical mode and a nonlinear transmon–mechanical mode interaction in the strong coupling regime. Together with the strong resonator–transmon interaction, these properties provide intriguing opportunities for manipulations of this hybrid quantum system. We show, in particular, the feasibility of cooling the mechanical motion down to its ground state and preparing various nonclassical states including mechanical Fock and cat states and hybrid tripartite entangled states.

Control of microwave signals using circuit nano-electromechanics

  1. Xiaoqing Zhou,
  2. Fredrik Hocke,
  3. Albert Schliesser,
  4. Achim Marx,
  5. Hans Huebl,
  6. Rudolf Gross,
  7. and Tobias J. Kippenberg
and circuit quantum electrodynamics (cQED) [2]. Coupled to artificial atoms in the form of superconducting"]qubits [3, 4], they now provide a technologically promising and scalable platform for quantum information processing tasks [2, 5-8]. Coupling these circuits, in situ, to other quantum systems, such as molecules [9, 10], spin ensembles [11, 12], quantum dots [13] or mechanical oscillators [14, 15] has been explored to realize hybrid systems with extended functionality. Here, we couple a superconducting coplanar waveguide resonator to a nano-coshmechanical oscillator, and demonstrate all-microwave field controlled slowing, advancing and switching of microwave signals. This is enabled by utilizing electromechanically induced transparency [16-18], an effect analogous to electromagnetically induced transparency (EIT) in atomic physics [19]. The exquisite temporal control gained over this phenomenon provides a route towards realizing advanced protocols for storage of both classical and quantum microwave signals [20-22], extending the toolbox of control techniques of the microwave field.