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Quantum Backaction Evading Measurements

The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum backaction of the measurement. Some measurement techniques, however, rely on coupling a probe to the system in such a way that the measured observable is an invariant of the Hamiltonian evolution, which allows to preserve the state of at least this observable. These are often called quantum nondemolition measurements, or quantum backaction evading (BAE) measurements. An example is the measurement of only a single quadrature of the oscillator, which can evade the backaction and thus can be carried out with arbitrary precision.

We have extended the scope of BAE measurements to a new class of systems with a high degree of coherence and therefore immediately adapted to force or metric sensing. As the mechanical oscillator, we use a large 0.5 mm diameter silicon nitride (SiN) membrane oscillator with 707 kHz frequency, embedded in a microwave cavity. High-stress SiN has emerged as the material to realize the highest mechanical quality factors for usage in quantum optomechanics. The measurement shows that quantum backaction noise can be evaded in the quadrature measurement of the motion of a large object.

• Quantum backaction evading measurements of a silicon nitride membrane resonator. .
   

We have demonstrated quantum backaction evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic mechanical entanglement and force sensing beyond conventional quantum limits.

• Quantum Backaction Evading Measurement of Collective Mechanical Modes. .

Microwave signal processing

Besides studying fundamental quantum concepts such as entanglement and backaction evasion, microwave optomechanics can be utilized for signal processing.

We have demonstrated that microwave optomechanical systems can be used as ultra-low-noise microwave amplifiers. In a phase-preserving mode the incoming microwave signal can be amplified while adding only half a quantum of noise, the minimum amount required by Heisenberg's uncertainty principle. When configured as a phase-senstive amplifier, the device amplifies a single quadrature of the incoming signal while adding almost no noise at all. The novel type of amplifiers may offer improved performance for information processing in certain applications.

Additionally, we have investigated nonreciprocal (i.e., directional) transport and amplification of electromagnetic or mechanical signals.

• Nonreciprocal transport based on cavity Floquet modes in optomechanics. .
• Noiseless Quantum Measurement and Squeezing of Microwave Fields Utilizing Mechanical Vibrations. . See also: .
• Low-Noise Amplification and Frequency Conversion with a Multiport Microwave Optomechanical Device. .
• Microwave amplification with nanomechanical resonators. .

Quantum systems with different types of degrees of freedom can intertwine, forming hybrid states with intriguing properties. We have explored setups for coupling transmon qubits to either low-frequency flexural resonators, or GHz-regime micro acoustic overtone (HBAR) resonances.

In a HBAR system, the modes mostly reside in the substrate chip and hence feature diluted strain and low acoustic losses. The system exhibits a dense spectrum of acoustic modes that interact near resonance with the qubit, suggesting a possibility to manipulate the many-mode system through the qubit. We have shown a qubit-HBAR system by controlling the qubit with longitudinal fields, allowing individually access a large number of acoustic modes.

• Coupling high-overtone bulk acoustic wave resonators via superconducting qubits. .
• Sideband control of a multimode quantum bulk acoustic system. .
• Landau-Zener-Stückelberg interference in a multimode electromechanical system in the quantum regime. .
• Hybrid circuit cavity quantum electrodynamics with a micromechanical resonator. .