Nonlinear Nanomechanical Resonator Research Articles

Nonlinear nanomechanical resonators approaching the quantum ground state

It is an open question whether mechanical resonators can be made nonlinear with vibrations approaching the quantum ground state. This requires the engineering of a mechanical nonlinearity far beyond what has been realized so far. Here we discover a mechanism to boost the Duffing nonlinearity by coupling the vibrations of a nanotube resonator to single-electron tunnelling and by operating the system in the ultrastrong-coupling regime. We find that thermal vibrations become highly nonlinear when lowering the temperature. The average vibration amplitude at the lowest temperature is 13 times the zero-point motion, with approximately 42% of the thermal energy stored in the anharmonic part of the potential. Our work may enable the realization of mechanical Schrödinger cat states, mechanical qubits and quantum simulators emulating the electron–phonon coupling.

Highly Sensitive Implementation of Logic Gates with a Nonlinear Nanomechanical Resonator

We introduce a theoretical concept of logic gates for sequenced data that contain a large number of data bits to be computed using a nonlinear nanomechanical resonator. Resonantly driven nanomechanical modes display the bistability of forced vibrations. Near the cusp point on the bifurcation curve, even a small change in driving force can lead to switching between the vibrational states with significantly different amplitudes. This enables a highly sensitive implementation of logic gates, including and, or, and xor gates. The underlying principles are simple and generic, suggesting that our method is applicable not only to nanomechanical systems but also to a wide variety of bistable physical, chemical, and biological systems.

An ultrathin integrated nanoelectromechanical transducer based on hafnium zirconium oxide

The monolithic integration of electromechanical transduction at the nanoscale with advanced CMOS is among the most important challenges of semiconductor electronic systems to leverage the multi-domain sensing, actuation, and resonance properties of nano-mechanical systems. Here we report on the demonstration of vibrating devices enabled by atomically engineered ferroelectric Hf0.5Zr0.5O2 thin films with a variety of mechanical resonance modes with frequencies (f0) between 340kHz - 13GHz and frequency-quality (Q) factor products (f0 x Q) up to 3.97 x 10^12. Experiments based on electrical and optical probing elucidate and quantify the role of the electrostrictive effect in the electromechanical transduction behavior of the Hf0.5Zr0.5O2 film. We further demonstrate the role of nonlinear electromechanical scattering on the operation of Hf0.5Zr0.5O2 transduced resonators. This investigation also highlights the potential of atomically engineered ferroelectric Hf0.5Zr0.5O2 transducers for new classes of CMOS-monolithic linear and nonlinear nanomechanical resonators in centimeter- and millimeter-wave frequencies.

Probing Nonclassicality of Two-Mode SU(2) Generator Based on Quantum Fisher Information* *Supported by the National Natural Science Foundation of China under Grant No. 11365006 and the Natural Science Foundation of Guizhou Province under Grant No. QKHLHZ[2015]7767

Nonclassicality is an essential but still open question in quantum mechanics. Here, utilizing the maximum value of quantum Fisher information, we suggest a new version of the nonclassical criterion for SU(2) generator realized by two bosonic modes. As an application of the criterion, the system of two coupled nonlinear nanomechanical resonators is considered. And the nonclassicality of the phonon state in the dynamical evolution is explored. The system has a dynamical phase transition from the tunnelling phase to the self-trapping phase by tuning the coupling strength. It is found that for the tunnelling phase, the phonon state is nonclassical in the full time evolution. And for the self-trapping phase, the evolved phonon state is still nonclassical in the full time with a relatively large coupling strength, while it is nonclassical i n the most of time (but not all) with a small coupling strength. Quantum coherence has distinct different behaviors in the two phases.

Driven nonlinear nanomechanical resonators as digital signal detectors

Because of their nonlinearity, vibrational modes of resonantly driven nanomechanical systems have coexisting stable states of forced vibrations in a certain range of the amplitude of the driving force. Depending on its phase, which encodes binary information, a signal at the same frequency increases or decreases the force amplitude. The resulting force amplitude can be outside the range of bistability. The values of the mode amplitude differ significantly on the opposite sides of the bistability region. Therefore the mode amplitude is very sensitive to the signal phase. This suggests using a driven mode as a bi-directional bifurcation amplifier, which switches in the opposite directions depending on the signal phase and provides an essentially digital output. We study the operation of the amplifier near the critical point where the width of the bistability region goes to zero and thus the threshold of the signal amplitude is low. We also develop an analytical technique and study the error rate near the threshold. The results apply to a broad range of currently studied systems and extend to micromechanical systems and nonlinear electromagnetic cavities.

Measuring Frequency Fluctuations in Nonlinear Nanomechanical Resonators.

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS2 and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive to date. In this article we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly clamped beams, in a cryogenic environment. We report on the same T/ f dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected damping fluctuations, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure δ f/ f0 lies in the range 0.5-0.01 ppm (consistent with the literature for cryogenic MHz devices) and decreases with mode number in the range studied. The technique can be applied to any type of nanomechanical structure, enabling progress toward the understanding of intrinsic sources of noise in these devices.

Phonon Josephson junction with nanomechanical resonators

We study coherent phonon oscillations and tunneling between two coupled nonlinear nanomechanical resonators. We show that the coupling between two nanomechanical resonators creates an effective phonon Josephson junction which exhibits two different dynamical behaviors: Josephson oscillation (phonon-Rabi oscillation) and macroscopic self-trapping (phonon blockade). Self-trapping originates from mechanical nonlinearities, meaning that when the nonlinearity exceeds its critical value, the energy exchange between the two resonators is suppressed, and phonon-Josephson oscillations between them are completely blocked. An effective classical Hamiltonian for the phonon Josephson junction is derived and its mean-field dynamics is studied in phase space. Finally, we study the phonon-phonon coherence quantified by the mean fringe visibility, and show that the interaction between the two resonators may lead to the loss of coherence in the phononic junction.

Tunable multiphonon blockade in coupled nanomechanical resonators

A single phonon in a nonlinear nanomechanical resonator (NAMR) can block the excitation of a second phonon [Phys. Rev. A 82, 032101 (2010)]. This intrinsically quantum effect is called phonon blockade, and is an analog of Coulomb blockade and photon blockade. Here we predict tunable multiphonon blockade in coupled nonlinear NAMRs, where nonlinearity is induced by two-level systems (TLSs) assuming dispersive (far off-resonance) interactions. Specifically, we derive an effective Kerr-type interaction in a hybrid system consisting of two nonlinearly-interacting NAMRs coupled to two TLSs and driven by classical fields. The interaction between a given NAMR and a TLS is described by a Jaynes-Cummings-like model. We show that by properly tuning the frequency of the driving fields one can induce various types of phonon blockade, corresponding to the entangled phonon states of either two qubits, qutrit and quartit, or two qudits. Thus, a $k$-phonon Fock state (with $k=1,2,3$) can impede the excitation of more phonons in a given NAMR, which we interpret as a $k$-phonon blockade (or, equivalently, phonon tunneling). Our results can be explained in terms of resonant transitions in the Fock space and via phase-space interference using the $s$-parametrized Cahill-Glauber quasiprobability distributions including the Wigner function. We study the nonclassicality, entanglement, and dimensionality of the blockaded phonon states during both dynamics and in the stationary limits.

Nonlinearity and nonclassicality in a nanomechanical resonator

We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems.

Quantum Decoherence of Charge Qubit Coupled to Nonlinear Nanomechanical Resonator

When the nonlinearity of nanomechanical resonator is not negligible, the quantum decoherence of charge qubit is studied analytically. Using nonlinear Jaynes—Cummings model, one explores the possibility of being quantum data bus for nonlinear nanomechanical resonator, the nonlinearity destroys the dynamical quantum information-storage and maintains the revival of quantum coherence of charge qubit. With the calculation of decoherence factor, we demonstrate the influence of the nonlinearity of nanomechanical resonator on engineered decoherence of charge qubit.

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semiclassical approximation of this system has an interesting fixed-point bifurcation structure. In the semiclassical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positive to negative detuning. We show that signatures of this bifurcation structure are also present in the full dissipative quantum system and further show that the bifurcation structure leads to mixed-state entanglement between the nanomechanical resonator and the microwave cavity in the dissipative quantum system that is a maximum close to the semiclassical bifurcation. Quantum signatures of the semiclassical limit cycles are presented.

Jahn-Teller instability in dissipative quantum systems

We consider the steady states of a harmonic oscillator coupled so strongly to a two-level system (a qubit) that the rotating wave approximation cannot be made. The Hamiltonian version of this model is known as the $E\otimes\beta$ Jahn-Teller model. The semiclassical version of this system exhibits a fixed point bifurcation, which in the quantum model leads to a ground state with substantial entanglement between the oscillator and the qubit. We show that the dynamical bifurcation survives in a dissipative quantum description of the system, amidst an even richer bifurcation structure. We propose two experimental implementations of this model based on superconducting cavities: a parametrically driven nonlinear nanomechanical resonator coupled capacitively to a coplanar microwave cavity and a superconducting junction in the central conductor of a coplanar waveguide.

Signal Amplification by 1/f Noise in Silicon-Based Nanomechanical Resonators

We report signal amplification by 1/f(alpha) noise with stochastic resonance in a nonlinear nanomechanical resonator. The addition of 1/f(alpha) noise to a subthreshold modulation signal enhances the probability of an electrostatically driven resonator switching between its two vibrational states in the hysteretic region. Considering the prevalence of 1/f noise in the materials in integrated circuits, signal enhancement demonstrated here, using a fully on-chip electronic actuation/detection scheme, suggests beneficial use of the otherwise detrimental noise.

Classical to quantum transition of a driven nonlinear nanomechanical resonator

Much experimental effort is invested these days in fabricating nanoelectromechanical systems (NEMS) that are sufficiently small, cold and clean, so as to approach quantum mechanical behavior as their typical quantum energy scale becomes comparable with that of the ambient thermal energy kBT. Such systems will hopefully enable one to observe the quantum behavior of human-made objects, and test some of the basic principles of quantum mechanics. Here, we expand and elaborate on our recent suggestion (Katz et al 2007 Phys. Rev. Lett. 99 040404) to exploit the nonlinear nature of a nanoresonator in order to observe its transition into the quantum regime. We study this transition for an isolated resonator, as well as one that is coupled to a heat bath at either zero or finite temperature. We argue that by exploiting nonlinearities, quantum dynamics can be probed using technology that is almost within reach. Numerical solutions of the equations of motion display the first quantum corrections to classical dynamics that appear as the classical-to-quantum transition occurs. This provides practical signatures to look for in future experiments with NEMS resonators.

Basins of Attraction of a Nonlinear Nanomechanical Resonator

We present an experiment that systematically probes the basins of attraction of two fixed points of a nonlinear nanomechanical resonator and maps them out with high resolution. We observe a separatrix which progressively alters shape for varying drive strength and changes the relative areas of the two basins of attraction. The observed separatrix is blurred due to ambient fluctuations, including residual noise in the drive system, which cause uncertainty in the preparation of an initial state close to the separatrix. We find a good agreement between the experimentally mapped and theoretically calculated basins of attraction.

Signatures for a Classical to Quantum Transition of a Driven Nonlinear Nanomechanical Resonator

We seek the first indications that a nanoelectromechanical system (NEMS) is entering the quantum domain as its mass and temperature are decreased. We find them by studying the transition from classical to quantum behavior of a driven nonlinear Duffing resonator. Numerical solutions of the equations of motion, operating in the bistable regime of the resonator, demonstrate that the quantum Wigner function gradually deviates from the corresponding classical phase-space probability density. These clear differences that develop due to nonlinearity can serve as experimental signatures, in the near future, that NEMS resonators are entering the quantum domain.

Noise Squeezing in a Nanomechanical Duffing Resonator

We study mechanical amplification and noise squeezing in a nonlinear nanomechanical resonator driven by an intense pump near its dynamical bifurcation point, namely, the onset of Duffing bistability. Phase sensitive amplification is achieved by a homodyne detection scheme, where the displacement detector's output, which has a correlated spectrum around the pump frequency, is down-converted by mixing with a local oscillator operating at the pump frequency with an adjustable phase. The down-converted signal at the mixer's output could be either amplified or deamplified, yielding noise squeezing, depending on the local oscillator phase.

Mass detection with a nonlinear nanomechanical resonator

Nanomechanical resonators having small mass, high resonance frequency, and low damping rate are widely employed as mass detectors. We study the performance of such a detector when the resonator is driven into a region of nonlinear oscillations. We predict theoretically that in this region the system acts as a phase-sensitive mechanical amplifier. This behavior can be exploited to achieve noise squeezing in the output signal when homodyne detection is employed for readout. We show that mass sensitivity of the device in this region may exceed the upper bound imposed by thermomechanical noise upon the sensitivity when operating in the linear region. On the other hand, we show that the high mass sensitivity is accompanied by a slowing down of the response of the system to a change in the mass.

Mechanical mixing in nonlinear nanomechanical resonators

The physics of nonlinear dynamics has been studied in detail in macroscopic mechanical systems like the driven classical pendulum. By now, it is possible to build mechanical devices on the nanometer scale with eigenfrequencies on the order of several 100 MHz. In this work, we want to present how to machine such nanomechanical resonators out of silicon-on-insulator wafers and how to operate them in the nonlinear regime in order to investigate higher-order mechanical mixing at radio frequencies. The nonlinear response then is compared in detail to nth-order perturbation theory and nonperturbative numerical calculations.