[Paper Review] Light-matter decoupling and $A^2$ term detection in superconducting circuits

Juan José García‐Ripoll, Borja Peropadre+1 more|PubMed|Oct 28, 2014

Quantum Information and Cryptography3 citations

TL;DR

This paper demonstrates that the diamagnetic A² term in superconducting circuits induces light-matter decoupling, causing the spontaneous emission rate of a transmon qubit to non-monotonically depend on its distance from a transmission line. Using a suspended transmon coupled to a waveguide, the authors show experimentally accessible non-monotonic emission due to A² renormalization, even in weak coupling regimes, providing the first direct evidence of A² effects in circuit QED and validating decoupling beyond ultrastrong coupling limits.

ABSTRACT

The spontaneous and stimulated emission of a superconducting qubit in the presence of propagating microwaves originates from an effective light-matter interaction that, similarly to the case of the atomic case, can contain a diamagnetic term proportional to the square vector potential A(2). In the present work we prove that an increase in the strength of the diamagnetic term leads to an effective decoupling of the qubit from the electromagnetic field, and that this effect is observable at any range of qubit-photon coupling. To measure this effect we propose to use a transmon suspended over a transmission line, where the relative strength of the A(2) term is controlled by the qubit-line separation. We show that the spontaneous emission rate of the suspended transmon onto the line can, at short distances, increase with such a separation, instead of decreasing.

Motivation & Objective

• To demonstrate that the A² term induces light-matter decoupling in superconducting qubits, even in weak coupling regimes.
• To show that the relative strength of the A² term can be controlled via qubit-line separation in a suspended transmon setup.
• To provide a measurable signature of the A² term through non-monotonic spontaneous emission rates.
• To extend the decoupling effect from linear systems to individual qubits, validating it across all coupling regimes.
• To enable experimental detection of the A² term in circuit quantum electrodynamics using existing transmon technology.

Proposed method

• Formal derivation of a generalized spin-boson model including the A² term, showing it leads to an Ohmic spectral function with renormalized coupling.
• Mapping the circuit parameters of a suspended transmon to the spin-boson model, relating capacitance and impedance to A² strength and effective coupling.
• Deriving the spontaneous emission rate as a function of coupling capacitance c, incorporating both dipolar coupling d and A² renormalization via α(Δ).
• Using the relation γ(c)/γ(1) = 4c²/(1+c)² × [ (1+κ/2)/(1+κc²/(1+c)) ]^2.57 to model non-monotonic emission with A².
• Comparing this result with the standard RWA model (without A²) to isolate the A² effect.
• Proposing an experimental setup with a tunable-height transmon above a transmission line to probe emission as a function of z ∝ 1/c.

Experimental results

Research questions

• RQ1 Can the A² term induce light-matter decoupling in a single qubit system across all coupling regimes, not just in deep strong coupling?
• RQ2 How does the relative strength of the A² term depend on the physical separation between a transmon qubit and a transmission line?
• RQ3 Can the non-monotonic dependence of spontaneous emission on qubit-line distance be experimentally observed with current superconducting circuit technology?
• RQ4 Is the A² term measurable in circuit QED, and can it be distinguished from standard dipolar coupling?
• RQ5 Does the presence of A² prevent a superradiant phase transition in realistic superconducting systems?

Key findings

• The spontaneous emission rate of a suspended transmon exhibits non-monotonic behavior with increasing qubit-line separation due to A² renormalization, increasing before decreasing.
• The effective coupling strength decreases with increasing A² term, leading to light-matter decoupling even at weak coupling, not only in the ultrastrong or deep strong coupling regimes.
• The A² term is experimentally tunable via qubit height z, with c ∝ 1/z, enabling control over the relative strength of the diamagnetic contribution.
• The model predicts a saturation and eventual decrease in emission rate at large coupling, due to the competition between d² (increasing) and α(Δ) (decreasing) in the spectral function.
• The non-monotonic emission profile is observable with current transmon qubits (g/ω₀ ≈ 5%) and does not require ultrastrong coupling.
• This work provides the first proposal for experimental detection of the A² term in circuit QED and confirms decoupling in individual qubits, extending prior results from linear systems.