Vortici quantizzati nei superfluidi bosonici: correzioni all’equazione di Gross-Pitaevskii

Il lavoro si propone di analizzare il comportamento di sistemi debolmente interagenti (gas di Bose diluiti ultrafreddi) a partire dall'equazione di Hartree e di Gross-Pitaevskii, ricavando l'equazione di Gross-Pitaevskii modificata nello spazio reciproco (MGPE). L'analisi della MGPE permetterà di descrivere il fenomeno dei vortici quantizzati nei conduttori di Bose-Einstein.ope

Non-linear Terahertz Driving of Plasma Waves in Layered Cuprates

The hallmark of superconductivity is the rigidity of the quantum-mechanical phase of electrons, responsible for superfluid behavior and Meissner effect. The strength of the phase stiffness is set by the Josephson coupling, which is strongly anisotropic in layered superconducting cuprates. So far, THz light pulses have been efficiently used to achieve non-linear control of the out-of-plane Josephson plasma mode, whose frequency scale lies in the THz range. However, the high-energy in-plane plasma mode has been assumed to be insensitive to THz pumping. Here, we show that THz driving of both low-frequency and high-frequency plasma waves is possible via a general two-plasmon excitation mechanism. The anisotropy of the Josephson couplings leads to marked differences in the thermal effects among the out-of-plane and in-plane response, consistently with the experiments. Our results link the observed survival of the in-plane THz non-linear driving above $T_c$ to enhanced fluctuating effects in the phase stiffness in cuprates, paving the way to THz impulsive control of phase rigidity in unconventional superconductors.Comment: 5 pages, 3 figure

Manipulating Plasma Excitations with Terahertz Light Pulses in Superconducting Cuprates

Layered cuprates offer a preferential playground for optical non-linearity thanks to the emergence, below Tc, of soft out-of-plane Josephson plasmons. The hallmark of such a non-linearity is the observation of Third Harmonic Generation, that has been theoretically understood as a sum-frequency process involving a two-plasmon excitation. However, recent experiments in cuprates with two planes per unit cell challenge this interpretation, due to the lack of resonant response at the temperature where the driving frequency matches the plasma energy scale, as observed instead in single-layer cuprates. Here we show that such an apparent discrepancy in bilayer systems can be resolved by taking into account the combined effect of light polarization and Josephson-coupling anisotropy on setting the energy range where three-dimensional layered plasma modes can be resonantly excited. Our results offer a novel perspective on the possibility to tune on demand high-harmonic generation by artificially designing Josephson heterostructures

Revealing novel aspects of light-matter coupling in terahertz two-dimensional coherent spectroscopy: the case of the amplitude mode in superconductors

Recently developed terahertz (THz) two-dimensional coherent spectroscopy (2DCS) is a powerful technique to obtain materials information in a fashion qualitatively different from other spectroscopies. Here, we utilized THz 2DCS to investigate the THz nonlinear response of conventional superconductor NbN. Using broad-band THz pulses as light sources, we observed a third-order nonlinear signal whose spectral components are peaked at twice the superconducting gap energy $2\Delta$. With narrow-band THz pulses, a THz nonlinear signal was identified at the driving frequency $\Omega$ and exhibited a resonant enhancement at temperature when $\Omega = 2\Delta$. General theoretical considerations show that such a resonance can only arise from a disorder-activated paramagnetic coupling between the light and the electronic current. This proves that the nonlinear THz response can access processes distinct from the diamagnetic Raman-like density fluctuations, which are believed to dominate the nonlinear response at optical frequencies in metals. Our numerical simulations reveal that even for a small amount of disorder, the $\Omega=2\Delta$ resonance is dominated by the superconducting amplitude mode over the entire investigated disorder range. This is in contrast to other resonances, whose amplitude-mode contribution depends on disorder. Our findings demonstrate the unique ability of THz 2DCS to explore collective excitations inaccessible in other spectroscopies

Terahertz displacive excitation of a coherent Raman-active phonon in V2O3

Nonlinear processes involving frequency-mixing of light fields set the basis for ultrafast coherent spectroscopy of collective modes in solids. In certain semimetals and semiconductors, generation of coherent phonon modes can occur by a displacive force on the lattice at the difference-frequency mixing of a laser pulse excitation on the electronic system. Here, as a low-frequency counterpart of this process, we demonstrate that coherent phonon excitations can be induced by the sum-frequency components of an intense terahertz light field, coupled to intraband electronic transitions. This nonlinear process leads to charge-coupled coherent dynamics of Raman-active phonon modes in the strongly correlated metal VO. Our results show an alternative up-conversion pathway for the optical control of Raman-active modes in solids mediated by terahertz-driven electronic excitation

Vortici quantizzati nei superfluidi bosonici: correzioni all’equazione di Gross-Pitaevskii

Il lavoro si propone di analizzare il comportamento di sistemi debolmente interagenti (gas di Bose diluiti ultrafreddi) a partire dall'equazione di Hartree e di Gross-Pitaevskii, ricavando l'equazione di Gross-Pitaevskii modificata nello spazio reciproco (MGPE). L'analisi della MGPE permetterà di descrivere il fenomeno dei vortici quantizzati nei conduttori di Bose-Einstein

Non-linear Terahertz driving of plasma waves in layered cuprates

Josephson coupling determines the superconducting phase stiffness and sets the energy scale of plasma waves. Here, the authors show that THz light can induce two-plasmon excitations of both out-of-plane and in-plane phase modes, leading however to markedly different resonant and thermal effects due to the strong anisotropy of the Josephson couplings

Theory of coherent-oscillations generation in terahertz pump-probe spectroscopy: from phonons to electronic collective modes

Time-resolved spectroscopies using intense THz pulses appear as a promising tool to address collective electronic excitations in condensed matter. In particular, recent experiments showed the possibility to selectively excite collective modes emerging across a phase transition, as is the case for superconducting and charge-densitywave (CDW) systems. One possible signature of these excitations is the emergence of coherent oscillations of the differential probe field in pump-probe protocols. While the analogy with the case of phonon modes suggests that the basic underlying mechanism should be a sum-frequency stimulated Raman process, a general theoretical scheme able to describe the experiments and to define the relevant optical quantity is still lacking. Here we provide this scheme by showing that coherent oscillations as a function of the pump-probe time delay can be linked to the convolution in the frequency domain between the squared pump field and a Raman-like nonlinear optical kernel. This approach is applied and discussed in a few paradigmatic examples: ordinary phonons in an insulator, and collective charge and Higgs fluctuations across a superconducting and a CDW transition. Our results not only account very well for the existing experimental data in a wide variety of systems, but they also offer a useful perspective to design future experiments in emerging materials

Raman Response in the Nematic Phase of FeSe

Raman experiments on bulk FeSe revealed that the low-frequency part of the B1g Raman response R_B1g(Ω), which probes nematic fluctuations, rapidly decreases below the nematic transition at Tn ∼ 85 K. Such behavior is expected when a gap opens up and at a first glance is inconsistent with the fact that FeSe remains a metal below Tn. We argue that the drop of R_B1g(Ω) can be ascribed to the fact that the nematic order drastically changes the orbital content of low-energy excitations near hole and electron pockets, making them nearly mono-orbital. In this situation, the B1g Raman response gets reduced by the same vertex corrections that enforce charge conservation in the symmetric Raman channel. The reduction holds at low frequencies and gives rise to gaplike behavior of R_B1g(Ω). We also show that the enhancement of the B1g Raman response near Tn is consistent with the sign change of the nematic order parameter between hole and electron pockets

THz non-linear optical response in cuprates: predominance of the BCS response over the Higgs mode

Recent experiments with strong THz fields in unconventional cuprate superconductors have clearly evidenced an increase of the non-linear optical response below the superconducting critical temperature Tc. As in the case of conventional superconductors, a theoretical estimate of the various effects contributing to the non-linear response is needed in order to interpret the experimental findings. Here, we report a detailed quantitative analysis of the non-linear THz optical kernel in cuprates within a realistic model, accounting for the band structure and disorder level appropriate for these systems. We show that the BCS quasiparticle response is the dominant contribution for cuprates, and its polarization dependence accounts very well for the third-harmonic generation measurements. On the other hand, the polarization dependence of the THz Kerr effect is only partly captured by our calculations, suggesting the presence of additional effects when the system is probed using light pulses with different central frequencies