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Fermionic Stoner-Dicke phase transition in Circuit Quantum Magnetostatics

Adel Ali, Alexey Belyanin

Abstract

We present a minimal tunable many-body system of fermions coupled to quantum magnetic flux, which is analytically diagonalizable and exhibits a variety of many-body phenomena such as Stoner orbital instability and Dicke-like quantum phase transition. In contrast to standard cavity quantum electrodynamics with its electric-dipole coupling of the electric field operators with matter, here it is the quantized magnetic field of an LC-resonator which is coupled to the angular momentum of particles. Adding the Josephson junction (JJ) to the linear LC circuit allows us to explore nonlinear flux-matter phases and sector-selective photon dressing in regimes relevant to circuit QED and mesoscopic rings. Furthermore, we consider the tight-binding systems that exhibit a tunable nonlinearity representing artificial JJ, but without actual JJs included in the circuit.

Fermionic Stoner-Dicke phase transition in Circuit Quantum Magnetostatics

Abstract

We present a minimal tunable many-body system of fermions coupled to quantum magnetic flux, which is analytically diagonalizable and exhibits a variety of many-body phenomena such as Stoner orbital instability and Dicke-like quantum phase transition. In contrast to standard cavity quantum electrodynamics with its electric-dipole coupling of the electric field operators with matter, here it is the quantized magnetic field of an LC-resonator which is coupled to the angular momentum of particles. Adding the Josephson junction (JJ) to the linear LC circuit allows us to explore nonlinear flux-matter phases and sector-selective photon dressing in regimes relevant to circuit QED and mesoscopic rings. Furthermore, we consider the tight-binding systems that exhibit a tunable nonlinearity representing artificial JJ, but without actual JJs included in the circuit.
Paper Structure (23 sections, 113 equations, 3 figures)

This paper contains 23 sections, 113 equations, 3 figures.

Table of Contents

  1. Electrons on a ring
  2. Zeeman coupling to electron spins
  3. Graphene ring coupled to quantized flux
  4. Mode elimination and effective interaction.
  5. Balanced versus polarized ground state and the critical point.
  6. Flux displacement across the transition.
  7. The nonlinear cavity
  8. Synthetic Josephson junction in tight-binding systems
  9. Model and sector reduction at arbitrary coupling
  10. Flux-qubit (rf-SQUID) mapping
  11. Conclusions
  12. Fermionic Phase Transition
  13. The Balanced Phase
  14. The Polarized Phase
  15. The Phase Transition Condition
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Sketches of a coupled QR--superconducting LC loop system. (a) Top view with the QR (red circle) inside the LC loop. (b) Side view: the QR above can be positioned at variable distance $h$ from a superconducting loop, e.g., by using a spacer layer, to control coupling.
  • Figure 2: Schematic of the ground state filling for (a) balanced and (b) polarized electron configurations.
  • Figure 3: Oscillator frequency $\Omega(M)$ normalized by $\omega_p$ as a function of the total orbital moment $M$ for the anharmonic LC mode. The frequency $\Omega(M) = 4\sqrt{A B_{\mathrm{eff}}(M)}$ is obtained from the curvature of the displaced quartic potential around its $M$-dependent minimum $x_0(M)$. Parameters (in units where $\hbar\omega_p = 1$) are $A = \hbar\omega_p/4$, $B = \hbar\omega_p/4 + g\phi^2 N$, $C = 2g\phi$, with $g = 0.2$, $\phi = 0.5$, $N = 20$, and $\alpha_4 = 0.02$. The mode is softest near $M = 0$ and stiffens symmetrically as $|M|$ increases due to the quartic nonlinearity.