Quantum noise in nonlinear nanoscale systems out of equilibrium

Abstract

In this thesis the quantum noise properties of the driven nonlinear oscillators under nonequilibrium conditions is studied in different physical situations.

We first consider a Duffing oscillator in the deep quantum regime being a monostable anharmonic oscillator which has a Kerr nonlinearity. In this system, we analyse the power spectrum of the photon number fluctuations induced by the coupling of the system to a dissipative environment. In the weak coupling regime of the environment, a weak Kerr nonlinearity, a weak amplitude modulation, and close to resonance we resort to the rotating wave approximation to solve the dissipative dynamics by solving the Lindblad quantum master equation and thereafter calculating the noise by means of the regression theorem. Both analytical and numerical calculations are presented, revealing a rich phenomenology. Most interestingly, we find that the dynamics of the photon number fluctuations is characterized by multiphoton oscillations which manifest themselves as peaks in the noise spectrum $S(omega)$ of photon number. The peak intensity is proportional to the stationary occupation probability of the initial quasienergy state. Therefore, the noise spectrum offers a convenient way to directly probe the stationary distribution over all the quasienergy states. Exactly at a multiphoton resonance, the noise spectrum consists in a collection of pairs of related resonances which are located at opposite frequencies and which are equal in height. Each pair is associated to a multiphoton doublet. In spite of large fluctuations over the oscillator quasienergy, no quasielastic peak occurs at zero frequency. Finally, for a weakly detuned modulation or a stronger driving, the spectrum becomes asymmetric. Besides, an additional quasielastic peak appears at zero frequency which represents incoherent relaxation of the fluctuations towards the stationary state. The two inelastic peaks are symmetrically located at finite frequencies and their width determines the inverse of the dephasing time. In addition, the quasielastic peak at zero frequency represents incoherent relaxation with the inverse relaxation time given by its width. In the driven system, the appearance of a quasielastic peak depends on the intriguing interplay between the nonlinearity, the driving strength and the dissipation strength characterizing a full nonequilibrium situation.

In the aforementioned regime, we use the Duffing oscillator as amplifier of the quantum state of a qubit. There, we exploit sharp multiphoton resonances in the nonlinear oscillator in the detection/amplification of the states of the qubit. This concept is an extension of the case of a linear resonator. We find that the sharp resonant lines offer the advantage that only a few measurement cycles are necessary to ensure a large discrimination power of the measurement. Moreover, we calculate the relaxation rate of the qubit due to the coupling with the Duffing oscillator around a multiphoton resonance. Notably, the back-action of the resonator on the qubit is sufficiently weak, yielding to a good qubit-state measurement fidelity.

Finally, in the pursuit of a detection scheme for the multiphoton(phonon) transitions in the Duffing oscillator, we study the electric charge current flowing through a nanobeam, in its nonlinear regime, clamped to conducting leads. We start with the calculation of the electron-phonon interaction, considering the general case of a nanobeam in presence of an electric and magnetic field. For the sake of simplicity, we consider the magnetic field case, taking into account that the contribution from the electric field is just an imaginary part in the coupling constant. We find that in the driven case, for ac bias voltages in the leads, and in leading order in the coupling constant, the current drives directly the deflection of the nanobeam. In order to compute observables of interest we apply a real-time diagrammatic expansion in the tunneling coupling, leading to master equation for the reduced density matrix. In the high frequency approximation, and combining this with the rotating wave approximation, we calculate the current flowing through the nanobeam. The ac part shows characteristic antiresonant behaviour as a consequence of the multiphonon transition transition in the nanobeam.