Tunable strong nonlinearity of a micromechanical beam embedded in a dc-SQUID (original) (raw)
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Journal of Applied Physics, 2015
We report on the fabrication and measurement of a micromechanical beam embedded in a direct current superconducting quantum interference device (dc-SQUID) and placed in an externally applied magnetic field. The coupling to the SQUID alters the effective potential of the mechanical modes of the beam, in a manner similar to the optical spring effect. This effective potential induces on the modes a strong frequency shift and Duffing type nonlinearity, both of which can be tuned by controlling the applied flux and bias current of the SQUID. A semi-numerical theoretical analysis of the effective potential is found to be in partial agreement with measured results. When biasing the SQUID slightly above the transition to the resistive state and when the applied flux is tuned to half integer value in units of flux quantum, the effective potential becomes divergent. We show this by obtaining an analytical expression for the circulating current of the SQUID at this operating regime.
Nonlinear dynamics in a high-gain amplifier: the dc SQUID
Annalen der Physik, 2000
We study the detection of very weak time-periodic magnetic signals via a double-junction (dc) Superconducting Quantum Interference Device (SQUID). The device, represented by two coupled nonlinear differential equations for the quantum mechanical junction phase differences, admits long-time static or oscillatory solutions, the transition between them being easily controlled by experimentally accessible parameters. Gain is maximal when the device is tuned to the onset of the oscillatory solutions; i.e., when the minima in the 2D potential function disappear. We concentrate on the SQUID dynamics near this critical point and compute the oscillation frequency via a center manifold reduction of the full 2D dynamics. Knowing this frequency permits its exploitation as a detection/classification tool in magnetic remote sensing applications.
dc SQUIDs as linear displacement detectors for embedded micromechanical resonators
Comptes Rendus Physique, 2011
Superconducting quantum interference devices (SQUIDs) can detect tiny amounts of magnetic flux and are also used to study macroscopic quantum effects. We employ a dc SQUID as a linear detector of the displacement of an embedded micromechanical resonator with a femtometer sensitivity. We discuss the measurement method, including operation in high magnetic field and a cryogenic amplification scheme which allows us to reach a resolution which is only a factor 4.4 above the standard quantum limit.
Nonlinear Coupling between the Two Oscillation Modes of a dc SQUID
Physical Review Letters, 2011
We make a detailed theoretical description of the two-dimensional nature of a dc-SQUID, analyzing the coupling between its two orthogonal phase oscillation modes. While it has been shown that the mode defined as "longitudinal" can be initialized, manipulated and measured, so as to encode a quantum bit of information, the mode defined as "transverse" is usually repelled at high frequency and does not interfere in the dynamics. We show that, using typical parameters of existing devices, the transverse mode energy can be made of the order of the longitudinal one. In this regime, we can observe a strong coupling between these modes, described by an Hamiltonian providing a wide range of interesting effects, such as conditional quantum operations and entanglement. This coupling also creates an atomic-like structure for the combined two mode states, with a V-like scheme.
Physical Review E, 2006
Dynamical systems that operate near the onset of coupling-induced oscillations can exhibit enhanced sensitivity to external perturbations under suitable operating parameters. This cooperative behavior and the attendant enhancement in the system response ͑quantified here via a signal-to-noise ratio at the fundamental of the coupling-induced oscillation frequency͒ are investigated in this work. As a prototype, we study an array of dc superconducting quantum interference device ͑SQUID͒ rings locally coupled, unidirectionally as well as bidirectionally, in a ring configuration; it is well known that each individual SQUID can be biased through a saddle-node bifurcation to oscillatory behavior. We show that biasing the array near the bifurcation point of coupling-induced oscillations can lead to a significant performance enhancement.
Potential Characterization of a Double SQUID Device for Quantum Computing Experiments
IEEE Transactions on Applied Superconductivity, 2007
We report on experiments performed on a system consisting of a double SQUID (superconducting quantum interference device) built with gradiometer geometry. Two single-turn coils provide two independent control fluxes: one of these allows biasing the device and tilting the potential, while the other changes the barrier height of the potential. When the dynamics of the inner dc SQUID can be neglected, the free energy of the double SQUID, as a function of the internal magnetic flux, is just the corrugated parabola of an rf SQUID whose local minima represent metastable states for the system. Our analysis instead is substantially concerned with the interesting phenomenology generated by the static configurations of an internal two-junction interferometer and by the tunability of the internal loop inductance. Two readout systems are employed to thoroughly characterize the dynamics of our system. We investigate the dynamical response at temperatures low enough (tens of mK) to minimize the effects of thermal fluctuations concentrating the analysis on the aspects that could be relevant for macroscopic quantum coherence and computing. The results indicate that from the finite inductance of the inner loop originates a potential well generating competing processes with the tunneling between the two main wells of the rf-SQUID potential.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2011
We propose a theoretical scheme to show the possibility of generating motional nonlinear coherent states and their superposition for an undamped vibrating micromechanical membrane inside an optical cavity. The scheme is based on an intensity-dependent coupling of the membrane to the radiation pressure field. We show that if the cavity field is initially prepared in a Fock state, the motional state of the membrane may evolve from vacuum state to a special type of nonlinear coherent states. By examining the nonclassical properties of the generated state of the membrane, including the quadrature squeezing and the sub-Poissonian statistics, we find that by varying the Lamb-Dicke parameter and the membrane's reflectivity one can effectively control those properties. In addition, the scheme offers the possibility of generating various types of the so-called nonlinear multicomponent Schrödinger cat sates of the membrane. We also examine the effect of the damping of the cavity field on the motional state of the membrane. and entanglement at a macroscopic scale .
Quantum dynamics of a microwave-driven SQUID
Superconductor Science & Technology, 2003
In recent years, the quantum behaviour of Josephson devices has been the object of thorough experimental investigation, mainly with the objective of studying quantum mechanics in macroscopic objects. At present, the same quantum properties are being exploited with the aim of the physical implementation of quantum bits and quantum registers. Here we present measurements on a system containing potential qubits, namely a rf SQUID and a hysteretic dc SQUID, magnetically coupled, under microwave excitation; the devices are realized on a single chip with trilayer Nb/AlO x /Nb technology. On this system we have performed a set of measurements to test the dc SQUID response to short pulses of microwaves ranging from 2 to 32 GHz. A first analysis of our results indicates the presence of population oscillations in the hysteretic dc SQUID. This result is very promising in view of using SQUIDs for more complex qubits systems.
Tuning of Strong Nonlinearity in rf SQUID Meta-Atoms
2022
Strong nonlinearity of a self-resonant radio frequency superconducting quantum interference device (rf-SQUID) meta-atom is explored via intermodulation (IM) measurements. Previous work in zero dc magnetic flux showed a sharp onset of IM response as the frequency sweeps through the resonance. A second onset at higher frequency was also observed, creating a prominent gap in the IM response. By extending those measurements to nonzero dc flux, new dynamics are revealed, including: dc flux tunabililty of the aforementioned gaps, and enhanced IM response near geometric resonance of the rf-SQUID. These features observed experimentally are understood and analyzed theoretically through a combination of a steady state analytical modeling, and a full numerical treatment of the rf SQUID dynamics. The latter, in addition, predicts the presence of chaos in narrow parameter regimes. The understanding of intermodulation in rf-SQUID metamaterials is important for producing low-noise amplification of...
Constants of motion in the dynamics of a 2N-junction SQUID
Physics Letters A, 1995
We show that a 2N junction SQUID (Superconducting QUantum Interference Device) made of 2N overdamped, shunted, identical junctions may be described as a system having only 6 degrees of freedom for any N ≥ 3. This is achieved by means of the reduction introduced by Watanabe and Strogatz (Physica D, 74, (1994) 197) for series biased arrays. In our case 6 rather than 3 degrees of freedom are necessary to describe the system, due to the requirement of phase quantization along the superconducting loop constituting the device. Generalization to multijunction parallel arrays is straightforward.