We present a novel framework for controlling Higgs mode and vortex dynamics in superconductors using structured light. We propose a phenomenon analog of the Kapitza-Dirac effect in superconductors, where Higgs waves scatter off light-induced vortex lattices, generating interference patterns akin to matter wave diffraction. We also find that the vortices enable the linear coupling of Higgs mode to the electromagnetic field. This interplay between light-engineered Higgs excitations and emergent vortex textures opens a pathway to probe nonequilibrium superconductivity with unprecedented spatial and temporal resolution. Our results bridge quantum optics and condensed matter physics, offering new examples of quantum printing where one uses structured light to manipulate the collective modes in correlated quantum fluids.
We present a novel framework for controlling Higgs mode and vortex dynamics in superconductors using structured light. We propose a phenomenon analog of the Kapitza-Dirac effect in superconductors, where Higgs waves scatter off light-induced vortex lattices, generating interference patterns akin to matter wave diffraction. We also find that the vortices enable the linear coupling of Higgs mode to the electromagnetic field. This interplay between light-engineered Higgs excitations and emergent vortex textures opens a pathway to probe nonequilibrium superconductivity with unprecedented spatial and temporal resolution. Our results bridge quantum optics and condensed matter physics, offering new examples of quantum printing where one uses structured light to manipulate the collective modes in correlated quantum fluids.
The challenge of controlling the quantum states of matter via light has been at the forefront of modern research on driven quantum matter. We explore the imprinting effects of structured light on superconductors, demonstrating how the quantum numbers of light—specifically spin angular momentum, orbital angular momentum, and radial order—can be transferred to the superconducting (SC) order parameter and control vortex dynamics. Using Laguerre-Gaussian beams, we show that by tuning the quantum numbers and the amplitude of the electric field, it is possible to manipulate a variety of vortex dynamics, including breathing vortex pairs, braiding vortex pairs, vortex droplets, and swirling two-dimensional vortex rings. More complex structures of vortex clusters, such as vortex flake structures, and standing wave motions, also emerge under specific quantum numbers. These results demonstrate the ability to control SC vortex motion and phase structures through structured light, offering potential applications in quantum fluids and optical control of superconducting states. Our findings present a diagram that links light's quantum numbers to the resulting SC vortex dynamics, highlighting the capacity of light to transfer its symmetry onto superconducting condensates. We point out that this approach represents the extension of printing to quantum printing by light in a coherent state of electrons.
Light carrying orbital angular momentum (OAM)---known as vortex beams---has broadened the scope of understanding and applications of light's angular momentum. Optical tweezers using OAM, often referred to as optical spanners, have significantly expanded the tunability of optical manipulation. A key frontier now lies in understanding how vortex beams interact with quantum states of matter. In this work, we numerically investigate the dynamics of a superconductor under vortex beam illumination and demonstrate the transfer of angular momentum from light to the superconducting collective mode, resulting in mechanical rotation. Our findings open a pathway for optical manipulation in the quantum regime, which we term the quantum optical spanner.
Controlling the states of quantum systems is a subject of major interest for both fundamental science and technological development. In this thesis, we carry out theoretical studies on how this can be achieved using light, both of classical and of quantum mechanical nature. We study a driven cavity system, where the driving field is classical and the cavity field is quantum mechanical. We demonstrate how virtual scattering of driving photons inside the cavity via two-photon processes can induce controllable long-range electron interactions in two-dimensional materials. We show that both the strength and the sign of the interactions can be tuned by the driving parameters and that the interactions are not screened effectively except at very low frequencies. For realistic cavity parameters, driving-induced heating of the electrons by inelastic photon scattering is suppressed and coherent electron interactions dominate. When the interactions are attractive, they cause an instability in the Cooper channel at a temperature proportional to the square root of the driving intensity. Our results open up a new avenue for engineering quantum materials on-demand and the possibility of studying the effect of long-range interactions in condensed matter systems. Following that, we take a more general approach to investigate the effect of long-range density-density electron attractive interactions on a superconductor. We show that the low-lying excitations of a 2D conventional superconductor can be significantly altered by these long-range interactions. Using BCS theory, we find that these interactions combine non-linearly with the intrinsic local attractions of the superconductor to increase the Bogoliubov quasiparticle excitation energies, thus enlarging the superconducting gap. Moreover, we show how the long-range nature of the driven-cavity-induced attractions qualitatively changes the collective excitations of the superconductor. Specifically, they lead to the appearance of additional collective excitations of the excitonic modes. They further push the Higgs mode "in gap": it lies below the Bogoliubov quasiparticle continuum such that it cannot decay through the quasiparticle excitations.
Superconductivity is an electronic state of matter arising from the existence of a common wave function with a coherent phase extending on a truly macroscopic scale. One major manifestation of this striking quantum phenomenon is the dissipationless transport of electrical current, an asset deserving particular attention in the present times where the efficient energy distribution has become of utmost importance. Unfortunately, the motion of quantum units of magnetic flux (so-called vortices or fluxons), which is an unavoidable side-effect found in superconductors in the presence of transport currents and magnetic fields, severely limits the conditions to preserve dissipationless transport. This poses a challenge for achieving the functionalization of superconducting materials and threatens their spectrum of applications. It is widely known that any inhomogeneities (either material imperfections, or ones made artificially), which locally suppress superconductivity on the scale comparable to the core of the vortex, can pin the vortex and delay the onset of the vortex motion to higher applied currents. In recent years a substantial effort has been made to minimize the effects of current-induced vortex motion by tailoring arrays of artificial pinning centers. Besides improving the critical parameters of the superconducting state, a pinning matrix can be used for the manipulation of vortex matter, thus directly affecting the vortex dynamics, such as rectification of vortex motion under an ac drive (vortex diode) by introducing asymmetric pinning landscapes. In the literature one can find that the realization of the anchoring of the vortices can be based on nanostructured arrays of perforations, chemically grown defects, permanent nanomagnets, or even pinning sites produced by heavy ion bombardment. All of those realizations are based on a permanent imprint on the superconductor, without any possibility for subsequent modifications in the distribution and strength of the pinning. The principal objective of this thesis is to investigate the dynamical behavior of vortex matter under an entirely new kind of pinning landscape consisting of spatial and temporal modulation of the superconducting condensate. A particular case of spatial modulation is considered in a constricted structure where current lensing can cause extremely high vortex velocities. Subsequently, a time-dependent thermal potential introduced to the superconducting condensate will cause stroboscopic resonances during the vortex motion - a phenomenon that cannot be observed in the systems with static pinning imprints. Finally, a study of electronic gating is presented, where the local properties of superconductor, such as mean free path, or electronic band structure in general, can be influenced electronically. This is a completely unexplored interdisciplinary research topic, which will eventually allow one to manipulate individual vortices in superconducting materials by means of spatially confined and temporally controlled thermal and electromagnetic excitations. Furthermore, such techniques can provide one fundamental insight in different states of the vortex matter with respect to variation of the transport current, highly relevant for understanding the resistive state of superconducting materials and their applications.
Driven atomic Josephson junctions allow one to monitor phase-coherent dynamics with unprecedented control and flexibility of the system's physical conditions. While cold-atom manifestations of the Josephson effect have been extensively studied in a wide variety of settings, atomic Josephson junctions in synthetic electromagnetic fields remain largely unexplored. Here, we show that synthetic magnetic fields can induce Fraunhofer-like modulations of the critical current in atomic Josephson junctions. Although this effect presents analogies to the Fraunhofer patterns found in superconducting devices, distinctive features emerge due to the neutral nature of the superfluid. We investigate the underlying spatial interference mechanisms and elucidate the role of Josephson vortices in the formation of spatially modulated current distributions based on numerical simulations. Our results open up new avenues for matter-wave circuits to deepen our understanding of spatial coherence in Josephson junctions, which are fundamental to the development of novel quantum technologies.
This thesis reports on theoretical investigations of the ultrafast nonequilibrium dynamics in superconductors. In particular, two nonequilibrium scenarios are modeled by combining several analytical and numerical methods: transient superconducting phase transition and collective excitations of a superconducting condensate. In the first part of the thesis the possibility to induce singlet superconducting correlations far from equilibrium is explored by applying time-dependent Lanczos algorithm to the one-dimensional extended Hubbard model. Here, the system is driven into a nonequilibrium state by (i) interaction quench and (ii) quench by pulse. In both cases the buildup of the superconducting correlations is studied in view of several correlation functions. Moreover, a transient Meissner effect, which reflects fingerprints of the induced superconductivity, is observed in calculations of the important for experiments time-dependent optical conductivity. In addition, the differences between nonequilibrium dynamics of the extended Hubbard model initiated by interaction quench and by pulse quench are discussed in detail. The second part is devoted to the excitation of collective modes in a superconductor out of equilibrium. First of all, focus is given to the properties of collective modes close to equilibrium conditions, where a linearized response can be expected. Within the framework of the (Nambu-) matrix kinetic theory in the clean limit a comprehensive gauge-invariant description of the collective modes associated with phase fluctuations of the order parameter is analytically formulated for the generalized case of two- band superconducting systems. Particular emphasis is on the application to the recently discovered noncentrosymmetric superconductors. A detailed analysis of the collective modes includes specification of the gauge mode (common to all superconductors) and the Leggett mode (collective fluctuations of the interband phase difference), and investigation of their subtle interplay in view of validity of the charge conservation law and the participation in the Anderson-Higgs mechanism. Further, the nonequilibrium excitation of the superconducting gaps for the case of two-band superconductors with singlet pairing correlations is investigated in a view of optical pump-probe experiments. For this purpose a semi-numerical method based on the density- matrix theory is formulated. In this case additional amplitude (Higgs) modes were identified, which allow to directly detect the properties of the superconducting condensates as a function of time. Moreover, a new interplay between the phase (Leggett) and amplitude (Higgs) modes is studied in detail. In particular it was found that the nonadiabatic excitation process leads to strong coupling between both modes. Finally, based on calculations of the time-dependent optical conductivity the prediction is made that the coupled Higgs and Leggett modes can be clearly visible in the pump-probe absorption spectra.