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arXiv:2009.12428 · Physical review. B./Physical review. B

Enhancement of superconductivity with external phonon squeezing

Andrey Grankin, Mohammad Hafezi, Victor M. Galitski

Published Dec 3, 2021• 13 citations
arXivHTMLPDF

Abstract

Squeezing of phonons due to the nonlinear coupling to electrons is a way to enhance superconductivity as theoretically studied in a recent work [Kennes et al., Nat. Phys. 13, 479 (2017)]. We study quadratic electron-phonon interaction in the presence of phonon pumping and an additional external squeezing. Interference between these two driving sources induces a phase-sensitive enhancement of electron-electron attraction, which we find as a generic mechanism to enhance any boson-mediated interactions. The strongest enhancement of superconductivity is shown to be on the boundary with the dynamical lattice instabilities caused by driving. We propose several experimental platforms to realize our scheme.

DOI
10.1103/physrevb.104.l220503

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Squeezing of phonons due to the nonlinear coupling to electrons is a way to enhance superconductivity as theoretically studied in a recent work [Kennes et al., Nat. Phys. 13, 479 (2017)]. We study quadratic electron-phonon interaction in the presence of phonon pumping and an additional external squeezing. Interference between these two driving sources induces a phase-sensitive enhancement of electron-electron attraction, which we find as a generic mechanism to enhance any boson-mediated interactions. The strongest enhancement of superconductivity is shown to be on the boundary with the dynamical lattice instabilities caused by driving. We propose several experimental platforms to realize our scheme.
Quantum control of phonons has become a focus of attention for developing quantum technologies. Here, we present a proposal to realize phonon blockade in a quadratically coupled optomechanical system, where a strong nonlinear interaction between photons and phonons can be induced by an external field coherently driving the cavity and the effective coupling strength is tunable by adjusting the amplitude of the driving field. This optically induced nonlinearity is different from standard methods for the realization of phonon blockade, where the nonlinearity is achieved by coupling the mechanical system to superconducting qubits. We both analytically and numerically study the phonon statistical properties via the steady-state solution of the second-order correlation function and find phonon blockade can be efficiently realized for a large cooperativity of the system, which is achievable based on the optically enhanced nonlinear coupling and high quality mechanical system.
We have investigated the ground state of an electron-phonon system with strong electron-phonon interaction and a weak on-site Coulomb repulsion using the correlated squeezed-state approach. We have introduced a variational ground state in which the phonon subsystem is in a correlated squeezed state and the electron subsystem is in a superconducting pairing state. In addition to the anharmonicity of each phonon mode induced by the linear coupling with the electrons, the correlated squeezed state is able to take into account the nonlinearity of the induced interaction between different phonon modes beyond the Hartree approximation. Also, with optimal values of the variational parameters this trial state will by construction yield an energy lower than those obtained in previous studies, and thus our variational ansatz is a more stable ground state for this system. Furthermore, in this approximate ground state the reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is considerably weakened. This weakening of the reduction effect should, in turn, affect other physical properties of the system; for instance, it does suggest the possibility of higher critical temperatures for superconductivity in the strong-coupling limit where the superfluidlike bipolaronic superconductivity is supposed to occur.
We propose a scheme to significantly enhance the cross-Kerr (CK) nonlinearity between photons and phonons in a quadratically coupled optomechanical system (OMS) with two-photon driving. This CK nonlinear enhancement originates from the parametric-driving-induced squeezing and the underlying nonlinear optomechanical interaction. Moreover, the noise of the squeezed mode can be suppressed completely by introducing a squeezed vacuum reservoir. As a result of this dramatic nonlinear enhancement and the suppressed noise, we demonstrate the feasibility of the quantum nondemolition measurement of the phonon number in an originally weak coupled OMS. In addition, the photon-phonon blockade phenomenon is also investigated in this regime, which allows for performing manipulations between photons and phonons. This Letter offers a promising route towards the potential application for the OMS in quantum information processing and quantum networks.
The problem of phonon-mediated and phonon-free contributions to d-wave superconductivity in the two-dimensional Hubbard model has been addressed. Strong local correlations (U\ensuremath{\rightarrow}\ensuremath{\infty} limit) have been incorporated in the slave boson formulation. In order to consider electron-boson and electron-phonon coupling on equal footing, fluctuations of the auxiliary boson fields over their mean-field value have been introduced. The magnitude of effective pairing interactions derived with the help of a canonical transformation indicates that within the weak-coupling theory, phonon-mediated pairing plays a marginal role and can be dominated by a phonon-free pairing mechanism. On the other hand, in the strong-coupling limit (Eliashberg formulation), electron-phonon and electron-phonon-boson interactions can significantly enhance the superconducting transition temperature. It is also shown that Coulomb correlations together with the electron-phonon interaction can effectively stabilize a d-wave superconducting state. \textcopyright{} 1996 The American Physical Society.
Studies on out-of-equilibrium dynamics have paved a way to realize a new state of matter. Superconductor-like properties above room temperatures recently suggested to be in copper oxides achieved by selectively exciting vibrational phonon modes by laser have inspired studies on an alternative and general strategy to be pursued for high-temperature superconductivity. We show that the superconductivity can be enhanced by irradiating laser to correlated electron systems owing to two mechanisms: First, the effective attractive interaction of carriers is enhanced by the dynamical localization mechanism, which drives the system into strong coupling regions. Second, the irradiation allows reaching uniform and enhanced superconductivity dynamically stabilized without deteriorating into equilibrium inhomogeneities that suppress superconductivity. The dynamical superconductivity is subject to the Higgs oscillations during and after the irradiation. Our finding sheds light on a way to enhance superconductivity that is inaccessible in equilibrium in strongly correlated electron systems.
Abstract In quantum materials, the electronic interaction and the electron-phonon coupling are, in general, two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, likely mediated by phonons, has been proposed in one-dimensional copper-oxide chain Ba2−xSrxCuO3+δ. Yet, it is unclear how this strong near-neighbor attraction V influences the superconductivity pairing in the system. Here we perform accurate many-body calculations to study the extended Hubbard model with on-site Coulomb repulsion U > 0 and near-neighbor attraction V < 0 that could well describe the cuprate chain and likely other similar transition-metal materials with both strong correlations and lattice effects. We find a rich quantum phase diagram containing an intriguing Tomonaga-Luttinger liquid phase — besides the spin density wave and various phase separation phases — that can host dominant spin-triplet pairing correlations and divergent superconductive susceptibility. Upon doping, the spin-triplet superconducting regime can be further broadened, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate chains.