High-harmonic spectroscopy of quantum phase transitions in a high-Tc superconductor

We report on the nonlinear optical signatures of quantum phase transitions in the high-temperature superconductor YBCO, observed through high harmonic generation. While the linear optical response of the material is largely unchanged when cooling across the phase transitions, the nonlinear optical response sensitively imprints two critical points, one at the critical temperature of the cuprate with the exponential growth of the surface harmonic yield in the superconducting phase and another critical point, which marks the transition from strange metal to pseudogap phase. To reveal the underlying microscopic quantum dynamics, a strong-field quasi-Hubbard model was developed, which describes the measured optical response dependent on the formation of Cooper pairs. Further, the theory provides insight into the carrier scattering dynamics and allows us to differentiate between the superconducting, pseudogap, and strange metal phases. The direct connection between nonlinear optical response and microscopic dynamics provides a powerful methodology to study quantum phase transitions in correlated materials. Further implications are light wave control over intricate quantum phases, light–matter hybrids, and application for optical quantum computing.

Attosecond technology (1), specifically the process of high harmonic generation (HHG) (2–4), provides an all-optical probe of the microscopic dynamics of atoms, molecules, and solids. Shortly after the first observation of high harmonics in atoms, their generation was understood (4–6) as arising from electron recollision after strong field photoionization and excursion in the continuum. Since the harmonic signal strongly depends on the electron recollision angle and time, high-harmonic spectroscopy (HHS) is a sensitive nonlinear probe of microscopic electronic structure with atomic spatial and suboptical cycle temporal resolution. HHS of solids (7, 8), two-dimensional materials (9, 10), or nanostructured media (11, 12) differs from the gas phase since the optical field–driven electronic wave packet is delocalized over many lattice sites, the wave function depends on the lattice momentum, and a hole has to match the electron’s momentum for recombination to occur (13, 14). Recent experimental efforts extended HHS as nonperturbative probe to quantum materials (9, 10, 15, 16) and to topological insulators (17–19). There have also been several theoretical advances, which suggest using strong fields to probe the physics of Mott insulators (20, 21), alongside the possibility of optically modifying strongly correlated matter (22) and tracking optically induced phase transitions (23), with a recent experiment reported in ref. 24.The sensitivity of HHS to the intricate microscopic details of carriers and lattice predestines HHS to investigate strong interactions and quantum correlations which lead to fascinating new states of matter such as superconductivity. The phase transition into a strongly correlated superconductive state is described by the spontaneous symmetry breaking of the U(1) redundancy when cooling below the critical temperature Tc of the material. As we will show, HHS is a sensitive probe of the dynamic evolution of the superconducting phase transition since the formation of composite bosons by pairing two fermionic spin-1/2 particles (Cooper pairs) changes the distribution of charge carriers, and this sensitively registers in the high harmonic amplitudes and spectral distribution. Pictorially, this is described in SI Appendix, Fig. S1, by a three-step model, consisting of 1) interband excitation process, 2) intraband acceleration, and 3) interband recombination. Pairing below T_c splits the bands by opening a superconducting gap Δ, and in the strongly correlated phase, the three processes of harmonic generation occur within the effective band structure for the Cooper pairs. We will also show that HHS can identify additional phase transitions between quantum phases in the strongly correlated material which are not accessible through the linear optical response, and they are difficult to detect with established methods such as superconducting quantum interference device (SQUID) magnetometry or four-probe transport measurements.A conventional superconductor can be described by the Anderson–Higgs mechanism, which explains that an optical nonlinear response is due to a gapless phase mode (Nambu–Goldstein) and a gapped amplitude mode (Higgs) of the ordering parameter. In the simplest case, and depending on the strength and type of excitation, Boltzmann and Ginzburg–Landau theories (25, 26) predict a second-order response, which mixes with the excitation mode (27, 28), thus the generation of the third harmonic (29). Unconventional high-Tc superconductors are of tremendous interest for a wide range of applications ranging from electronic devices and information processing devices to optical quantum computers and quantum simulators. However, due to their rich landscape of quantum phases and the difficulties of experimental methods to probe the microscopic dynamics, our understanding is still very limited.Among the well-established methods, e.g., transport measurements (30) or magnetic torque measurements (31, 32), photoemission measurements such as angle-resolved photoemission spectroscopy (ARPES) (33, 34) provide direct access to a material’s microscopic carrier distribution and dynamics. The interpretation of such ARPES measurement is, however, complicated by the interpretation of the bulk spectral function and the assumption of independent electron emission despite measuring a strongly correlated electronic state of matter. These are central questions to access the nature of the multibody state, which call for further developments and powerful new tools to aid in the interpretation of the physical mechanism.Therefore, the development of all-optical and ultrafast probes of the macroscopic dynamics inside such materials, which is compatible with existing methods, is highly desirable. To this aim, we apply HHS to investigate the transition between the different phases of the unconventional high-Tc superconductor YBa₂Cu₃O7−d (YBCO). We elucidate the connection between the measured optical spectra, the transition between strange metal and pseudogap phases, and the superconducting phase transition with a strong-field Hubbard model. The HHS measurement clearly shows a departure from the normal conducting phase with an increased formation of Cooper pairs upon cooling. The variation in harmonic orders is linked to phenomenological energy and phase relaxation times, which identify the transition to the fluctuation regime (35, 36), i.e., between the strange metal and pseudogap phases, and the sudden transition at Tc into the superconducting phase. Unconventional superconductors, like YBCO, are material systems in which the formation of composite bosons out of paired fermions is mediated not by phonon exchange but by some other kind of energy exchange (37), for instance, due to spin fluctuations. Such systems present many standing fascinating questions. It is thus important to have new powerful experimental techniques like HHS that provide a fresh and alternate view of the problem.     

Association of a TRAF1 and a STAT4 gene polymorphism with increased risk for rheumatoid arthritis in a genetically homogeneous population

Rheumatoid arthritis (RA) is a multifactorial disease that is increasing in incidence worldwide. It is associated with a complex mode of inheritance, with many genes being involved in the development and progression of the disease. Genome-wide association studies in different populations have recently revealed a significant association between a TRAF1/C5 and a STAT4 polymorphism and the development of RA. In the present study we performed a case-control study in the population of the island of Crete, Greece, aiming to replicate the former findings in a genetically homogeneous cohort of patients. We found that mutated allele A or genotypes A/A and G/A of the TRAF1/C5 rs10818488 SNP were more common in individuals with RA than in control individuals (odds ratio [OR] = 1.7, 95% confidence interval [CI] = 1.35-2.15, and OR = 2.22, 95% CI = 1.61-3.05, respectively). Similarly, mutated allele T or genotypes T/T and G/T of the STAT4 rs7574865 SNP were also associated with susceptibility to RA (OR = 1.9, 95% CI = 1.46-2.50, and OR = 2.37, 95% CI 1.73-2.25, respectively). Thus, we conclude that mutant alleles or genotypes of both polymorphisms examined are associated with the development of RA in our population.