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Zero-point energy of solids from vacuum fluctuation and quantum geometric force

Yugo Onishi, Liang Fu

Abstract

We show that quantum fluctuations of electromagnetic fields induce an additional zero-point energy in solids, which scales with the volume. For insulators, the zero-point energy density is proportional to quantum fluctuation of electric polarization in the many-body ground state, a fundamental quantum geometric property of solids known as the quantum weight. Although the zero-point energy does not affect the dynamics of the electromagnetic fields, when the fields are produced by a superconducting LC circuit, the zero-point energy contributes to a repulsive force between the circuit and the material. In addition, since zero-point energy depends on the circuit's capacitor, it yields a measurable static force acting on the capacitor plates, which we call quantum geometric force. The proposed effects provide direct experimental access to the many-body quantum geometry and reveal a new macroscopic quantum effect in solids induced by vacuum fluctuation.

Zero-point energy of solids from vacuum fluctuation and quantum geometric force

Abstract

We show that quantum fluctuations of electromagnetic fields induce an additional zero-point energy in solids, which scales with the volume. For insulators, the zero-point energy density is proportional to quantum fluctuation of electric polarization in the many-body ground state, a fundamental quantum geometric property of solids known as the quantum weight. Although the zero-point energy does not affect the dynamics of the electromagnetic fields, when the fields are produced by a superconducting LC circuit, the zero-point energy contributes to a repulsive force between the circuit and the material. In addition, since zero-point energy depends on the circuit's capacitor, it yields a measurable static force acting on the capacitor plates, which we call quantum geometric force. The proposed effects provide direct experimental access to the many-body quantum geometry and reveal a new macroscopic quantum effect in solids induced by vacuum fluctuation.
Paper Structure (7 sections, 55 equations, 3 figures)

This paper contains 7 sections, 55 equations, 3 figures.

Table of Contents

  1. Equivalence with the many-body quantum geometric tensor defined through the twisted boundary condition
  2. Effect of capacitive coupling
  3. Effective Hamiltonian
  4. Quantum geometric force including the effect of charge coupling
  5. Remark on systems with long-range Coulomb interaction
  6. Nonadiabatic correction
  7. Example: Superconducting resonator as a target

Figures (3)

  • Figure 1: (a) Interaction between a superconducting LC circuit and a quantum material. The magnetic flux $\hat{\varphi}$ behaves as a magnetic dipole moment and creates the vector potential $\vb*{A}$ on the electronic system. (b) The diamagnetic process due to the quantum fluctuation in the superconducting circuit. The flux $\varphi$ in the inductor induces the current $I_{\rm ind}$ in the electronic system, which results in a magnetic moment $m$ that is antiparallel to the flux $\varphi$, and thus increases the energy. The current $I$ accumulates the charge on the capacitor, resulting in an attractive force between the capacitor plates.
  • Figure 2: A possible experimental realization. (a) Measurement of the attractive quantum geometric force. The capacitor in the circuit is made of a mechanical resonator, so that it can move and detect the quantum geometric force. (b) Measurement of the repulsive quantum geometric force. SQUID is fabricated on a cantilever (SQUID-on-lever). SQUID acts as a LC circuit approximately, and the quantum fluctuation in SQUID induces the repulsive quantum geometric force when it is close contanct to the material.
  • Figure 3: Probing quantum metric with superconducting circuit. (a) A microwave resonator consisting of an inductor and a capacitor with an external magnetic flux $\phi_{\rm ext}$. (b) Two microwave resonators that are inductively coupled.