19 research outputs found
Classical many-body time crystals
Discrete time crystals are a many-body state of matter where the extensive
system's dynamics are slower than the forces acting on it. Nowadays, there is a
growing debate regarding the specific properties required to demonstrate such a
many-body state, alongside several experimental realizations. In this work, we
provide a simple and pedagogical framework by which to obtain many-body time
crystals using parametrically coupled resonators. In our analysis, we use
classical period-doubling bifurcation theory and present a clear distinction
between single-mode time-translation symmetry breaking and a situation where an
extensive number of degrees of freedom undergo the transition. We
experimentally demonstrate this paradigm using coupled mechanical oscillators,
thus providing a clear route for time crystals realizations in real materials.Comment: 23 pages, 5 figures, comments are welcom
The role of fluctuations in quantum and classical time crystals
Discrete time crystals (DTCs) are a many-body state of matter whose dynamics
are slower than the forces acting on it. The same is true for classical systems
with period-doubling bifurcations. Hence, the question naturally arises what
differentiates classical from quantum DTCs. Here, we analyze a variant of the
Bose-Hubbard model, which describes a plethora of physical phenomena and has
both a classical and a quantum time-crystalline limit. We study the role of
fluctuations on the stability of the system and find no distinction between
quantum and classical DTCs. This allows us to probe the fluctuations in an
experiment using two strongly coupled parametric resonators subject to
classical noise.Comment: 11 pages, 5 figure
Ghost in the Ising machine
Coupled nonlinear systems have promise for parallel computing architectures.
En route to realizing complex networks for Ising machines, we report an
experimental and theoretical study of two coupled parametric resonators
(parametrons). The coupling severely impacts the bifurcation topology and the
number of available solutions of the system; in part of the stability diagram,
we can access fewer solutions than expected. When applying noise to probe the
stability of the states, we find that the switching rates and the phase-space
trajectories of the system depend on the detuning in surprising ways. We
present a theoretical framework that heralds the existence of 'ghost
bifurcations'. These bifurcations involve only unstable solutions and lead to
avoided zones in phase space. The emergence of such ghost bifurcations is an
important feature of parametron networks that can influence their application
for parallel logic operations
Rapid flipping of parametric phase states
Since the invention of the solid-state transistor, the overwhelming majority
of computers followed the von Neumann architecture that strictly separates
logic operations and memory. Today, there is a revived interest in alternative
computation models accompanied by the necessity to develop corresponding
hardware architectures. The Ising machine, for example, is a variant of the
celebrated Hopfield network based on the Ising model. It can be realized with
artifcial spins such as the `parametron' that arises in driven nonlinear
resonators. The parametron encodes binary information in the phase state of its
oscillation. It enables, in principle, logic operations without energy transfer
and the corresponding speed limitations. In this work, we experimentally
demonstrate flipping of parametron phase states on a timescale of an
oscillation period, much faster than the ringdown time \tau that is often
(erroneously) deemed a fundamental limit for resonator operations. Our work
establishes a new paradigm for resonator-based logic architectures.Comment: 6 pages, 3 figure
Deterministic and stochastic sampling of two coupled Kerr parametric oscillators
The vision of building computational hardware for problem optimization has
spurred large efforts in the physics community. In particular, networks of Kerr
Parametric Oscillators (KPOs) are envisioned as simulators for finding the
ground states of Ising Hamiltonians. It was shown, however, that KPO networks
can feature large numbers of unexpected solutions that are difficult to sample
with the existing deterministic (i.e., adiabatic) protocols. In this work, we
experimentally realize a system of two coupled KPOs and find good agreement
with the predicted mapping to Ising states. We then introduce a protocol based
on stochastic sampling of the system and show how the resulting probability
distribution can be used to identify the ground state of the corresponding
Ising Hamiltonian. This method is akin to a Monte-Carlo sampling of multiple
out-of-equilibrium stationary states and is less prone to become trapped in
local minima than deterministic protocols
On the effect of linear feedback and parametric pumping on a resonators frequency stability
Resonant sensors based on Micro- and Nano-Electro Mechanical Systems (M/NEMS)
are ubiquitous in many sensing applications due to their outstanding
performance capabilities, which are directly proportional to the quality factor
(Q) of the devices. We address here a recurrent question in the field: do
dynamical techniques that modify the effective Q (namely parametric pumping and
direct drive velocity feedback) affect the performance of said sensors? We
develop analytical models of both cases, while remaining in the linear regime,
and introduce noise in the system from two separate sources: thermomechanical
and amplifier (read-out) noise. We observe that parametric pumping enhances the
quality factor in the amplitude response, but worsens it in the phase response
on the resonator. In the case of feedback, we find that Q is enhanced in both
cases. Then, we establish a solution for the noisy problem with direct drive
and parametric pumping simultaneously. We also find that, in the case when
thermomechanical noise dominates, no benefit can be obtained from neither
artificial Q-enhancement technique. However, in the case when amplifier noise
dominates, we surprisingly observe that a significant advantage can only be
achieved using parametric pumping in the squeezing region
The role of fluctuations in quantum and classical time crystals
Discrete time crystals (DTCs) are a many-body state of matter whose dynamics are slower than the forces acting on it. The same is true for classical systems with period-doubling bifurcations. Hence, the question naturally arises what differentiates classical from quantum DTCs. Here, we analyze a variant of the Bose-Hubbard model, which describes a plethora of physical phenomena and has both a classical and a quantum time-crystalline limit. Fluctuations enter the system due to the intrinsic quantum uncertainty and/or due to finite coupling to an environment. These fluctuations can activate transitions between the system's various stationary solutions. We study the role of fluctuations on the stability of the system in the long-time limit and find no distinction between quantum and classical DTCs. This allows us to probe the fluctuations in an experiment using two strongly coupled parametric resonators subject to classical noise
HarmonicBalance.jl : A Julia suite for nonlinear dynamics using harmonic balance
HarmonicBalance.jl is a publicly available Julia package designed to simplify and solve systems of periodic time-dependent nonlinear ordinary differential equations. Time dependence of the system parameters is treated with the harmonic balance method, which approximates the system's behaviour as a set of harmonic terms with slowly-varying amplitudes. Under this approximation, the set of all possible steady-state responses follows from the solution of a polynomial system. In HarmonicBalance.jl, we combine harmonic balance with contemporary implementations of symbolic algebra and the homotopy continuation method to numerically determine all steady-state solutions and their associated fluctuation dynamics. For the exploration of involved steady-state topologies, we provide a simple graphical user interface, allowing for arbitrary solution observables and phase diagrams. HarmonicBalance.jl is a free software available at https://github.com/NonlinearOscillations/HarmonicBalance.jl.publishe
Quantum Transducer Using a Parametric Driven-Dissipative Phase Transition
ISSN:0031-9007ISSN:1079-711