Optomechanical effects of two-level systems in a back-action evading measurement of micro-mechanical motion

Abstract

We show that the two-level systems (TLS) in lithographic superconducting circuits act as a power-dependent dielectric leading to non-linear responses in a parametrically coupled electromechanical system. Driven TLS shift the microwave resonance frequency and modulate the mechanical resonance through the optical spring effect. By pumping with two tones in a back-action evading measurement, these effects produce a mechanical parametric instability which limits single quadrature imprecision to 1.4 xzp. The microwave resonator noise is also consistent to a TLS-noise model. These observations suggest design strategies for minimizing TLS effects to improve ground-state cooling and quantum non-demolition measurements of motion.

Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the 3 dB Limit

“…2(c)]. Similar induced mechanical parametric driving has been observed in other BAE measurements; they can arise via a number of mechanisms including thermal effects as well as higher nonlinearities [28,29]. To understand the effects of this mechanical parametric driving, we phenomenologically add the mechanical parametric interaction to our otherwise ideal optomechanical model [30]:…”

“…However, the model does not fully capture the observed quadrature variance in the BAE measurement. The deviation may be due to the complicated heating effects associated with the underlaying nonlinearities [28,29] that cause the spurious mechanical parametric drive. We stress that our treatment of the spurious mechanical parametric drive is phenomenological; we do not know the precise microscopic mechanism which causes this driving.…”

Optomechanical backaction-evading measurement without parametric instability

“…However, even in carefully engineered devices, the limit in Eq. (2) is reached at low pump power, reducing the maximum possible accuracy of the backaction-evading measurement to above the zero-point level [11].…”

“…In the experiments mentioned above, it originated respectively from nonlinear terms in the optomechanical coupling [9], cavity heating causing a thermal shift in the frequency of the mechanical element [10], and two-level systems in surface oxides acting as nonlinear dielectrics [11]. Thus, the common limitation of these experiments is a connection between mechanical frequency and the cavity energy, δ m ∝ E. In the two-tone scheme, this connection seems to lead inevitably to parametric instability.…”

“…More recently, experiments have been carried out in the quantum regime. These have reached sensitivities of 4x zp [9], 2.5x zp [10], and 1.4x zp [11], but, thus far, no experiment has achieved sub-zero-point position sensitivity.…”