Collective Floquet engineering between two distant superconducting artificial atoms

AI summary

Overview

Research area: Superconducting circuit quantum electrodynamics (waveguide QED), Floquet engineering, and collective quantum optics with photon-mediated qubit–qubit interactions.

Technical level: Advanced. The paper relies on driven two-level-system physics, Bessel-function dressed couplings, master-equation modeling, and microwave reflection spectroscopy of transmons, though the central ideas are stated in physically transparent terms.

Scope: An experimental demonstration that periodic flux modulation of two superconducting qubits coupled to a mirror-terminated waveguide lets one dynamically tune both the coherent (virtual-photon) and dissipative (real-photon) parts of their photon-mediated interaction.

What This Paper Is About

When two qubits share a waveguide, they can exchange virtual photons (producing a coherent collective Lamb shift) or real photons (producing superradiant and subradiant collective decay). In a static device this interaction is frozen: it is set by qubit frequencies, qubit positions relative to the standing wave, and line couplings, and cannot be changed without physically altering the circuit. The paper's goal is to make that interaction dynamically controllable by periodically modulating the qubit frequencies (Floquet engineering), so the same chip can suppress, restore, or reshape the coupling on demand.

Key Contributions

1. A single device that hosts both coupling characters. By tuning the qubit operating frequency, the distant qubit sits either at a node of the standing wave (Hermitian coupling, HC, real coupling strength) or at an antinode (non-Hermitian coupling, NHC, purely imaginary coupling strength), on the same chip with the same two qubits.
2. Floquet control of the coherent coupling. Driving one qubit produces Floquet sidebands whose splittings are set by Bessel-dressed couplings $g_n = g_s J_n(f)$ with $f = \Delta_i/\nu$, allowing the collective Lamb shift to be tuned from its static value down to zero.
3. Floquet control of the dissipative coupling. In the antinode (NHC) configuration, the same Bessel factor modulates the collective radiative linewidths, so superradiant/subradiant decay can be tailored on demand.
4. A phase-only control knob. When both qubits are driven, the coupling becomes $g_n = g_s J_n[2f\sin(\theta/2)]$ with $\theta = \theta_d - \theta_m$, so the relative pump phase alone continuously tunes the interaction without changing qubit frequencies, spatial separation, or pump power.

Main Findings

• Static baseline established. One transmon ($Q_M$) sits at the mirror and always at an antinode; the other ($Q_D$) sits $L = 60$ mm away, within the Markovian regime ($2L/v \ll \Gamma_{10}^{-1}$), which the paper states as holding.
• Hermitian coupling at $f_1/2\pi = 4.527$ GHz. $Q_D$ is at a node and the coupling is real, $g_s = \sqrt{\Gamma_m(f_1)\Gamma_d(f_1)}$; the reflection spectrum shows an avoided crossing with splitting $2g_s$, revealing a collective Lamb shift comparable to twice the transition linewidth.
• Non-Hermitian coupling at $f_2/2\pi = 5.031$ GHz. $Q_D$ is at an antinode and $g_s = -i\sqrt{\Gamma_m(f_2)\Gamma_d(f_2)}$ is purely imaginary; the spectrum shows a level crossing with an enhanced collective linewidth rather than a coherent splitting.
• Coherent destruction of tunneling (CDT). The Floquet band splitting collapses at the zeros of $J_0(f)$ (marked by black arrows in the data), showing that virtual-photon exchange and the collective Lamb shift can be switched off while both qubits remain coupled to the same waveguide continuum.
• Power-controlled collapses and revivals. At fixed $\nu/2\pi = 11$ MHz, sweeping pump power produces the Bessel-function revivals and collapses; when $Q_D$ is driven at its node frequency, the driven qubit is not directly probed and the zeroth-band splitting maps cleanly onto $J_0(f)$.
• Dissipative channel modulated. In the NHC configuration the collective decay can be driven from enhanced collective emission to strong suppression. The paper notes that a weak stray resonance (visible near $\delta_p/2\pi = -21$ MHz and $44$ MHz, corresponding to $\omega_p/2\pi = 5.01$ GHz and $5.075$ GHz) obscures the direct linewidth signal in the raw data, so the linewidth modulation is established with numerical spectra in which this background is removed.
• Phase tuning demonstrated. At $P_\text{pump} \approx -72$ dBm and $-80$ dBm and $\nu/2\pi = 11$ MHz, the Floquet-band splitting recovers the static value near $\theta = 0$ and collapses at multiple phases near $J_0[2f\sin(\theta/2)] = 0$, in the HC configuration; the same Bessel factor modulates collective linewidths in the NHC configuration.
• Higher-order sidebands. At stronger driving, additional higher-order Floquet sidebands become visible in both HC and NHC configurations.
• Coupling character is inherited. The Hermitian or dissipative character of the static coupling is preserved in the driven system; the drive renormalizes the interaction amplitude rather than changing its nature.

Methodology in Plain English

The team fabricated two transmon-type artificial atoms on one chip, both capacitively coupled to a superconducting coplanar waveguide whose end is capacitively loaded to ground, acting as a mirror. That mirror sets up a standing wave, so a qubit's distance in wavelengths — adjustable by changing its frequency — decides whether it sits at a node or an antinode. The mirror qubit is fixed at an antinode; the distant qubit is 60 mm away and its frequency is tuned to reach either condition.

They probed the two-qubit system with a weak continuous-wave tone from a vector network analyzer and recorded the reflection coefficient, keeping the probe weak enough that it induces negligible population. A global magnetic coil and local flux lines set the qubit frequencies; the local lines also carry a sinusoidal pump tone that oscillates each qubit's frequency, with independently controlled power and phase. The measured reflection spectra versus probe detuning, pump frequency, pump power, and relative pump phase reveal Floquet sidebands and their Bessel-function envelopes. Supporting master-equation simulations, including Fourier expansion of the density matrix into Floquet components, reproduce the data and isolate features masked by stray resonances.

Why This Matters

Impact on research. The work turns a fixed geometric resource — waveguide-mediated qubit–qubit interaction — into a programmable one. It connects Floquet engineering, previously prominent in cold atoms, photonics, and magnonics, to waveguide QED, and shows that both coherent and dissipative collective effects can be addressed with the same knob. Switching between Hermitian and non-Hermitian coupling by frequency alone gives a clean testbed for driven-dissipative and non-Hermitian physics.

Real-world applications (as motivated in the paper):

• Suppressing idle crosstalk in distributed or modular quantum architectures by dynamically decoupling remote qubits without detuning or repositioning them.
• Quantum state transfer and remote entanglement generation in distributed quantum networks, including use of itinerant photons.
• Programmable spin–spin interactions for quantum simulation of many-body Hamiltonians, including models with engineered dissipation.
• On-demand control of collective radiative lifetimes, relevant wherever superradiance and subradiance are used as resources.

Industry relevance. Superconducting waveguide QED is a leading hardware route for quantum computing; a purely electrical, room-temperature-controlled knob for tuning nonlocal couplings and decay rates is attractive for scaling modular processors and for mitigating crosstalk in multi-chip architectures.

Future Directions

• Extending the scheme to larger qubit arrays, where Floquet-programmable couplings would implement dynamically reconfigurable spin models and entanglement distribution between many remote nodes.
• Exploring driven-dissipative many-body physics, including non-equilibrium phase transitions and topological phenomena in open quantum systems, which the paper names as an open frontier.
• Exploiting the non-Hermitian regime more fully, including exceptional-point physics and engineered dissipation, building on the ability to reach purely imaginary coupling.
• Improving device cleanliness at $f_2$ (the stray resonances at 5.01 GHz and 5.075 GHz currently mask the direct linewidth signal) so dissipative Floquet effects can be resolved without background subtraction, and pushing to stronger drives where higher-order Floquet channels proliferate.

Target Audience

Advanced graduate students and researchers in superconducting quantum circuits, waveguide QED, and Floquet/driven quantum systems; quantum-optics theorists interested in collective Lamb shifts and non-Hermitian couplings; and quantum-hardware engineers working on modular architectures, remote entanglement, and crosstalk mitigation. Readers without background in open quantum systems or microwave spectroscopy will find the experimental detail demanding, though the conceptual message is broadly accessible.

Authors’ abstract

A one-dimensional waveguide is a crucial medium for transferring propagating quantum information between remote qubits, yet the photon-mediated interaction is typically fixed by the static device geometry, qubit parameters, and their couplings to the transmission line. Such an interaction can be engineered to be coherent or dissipative via virtual- or real-photon exchange, respectively, yet its effective strength remains fixed in either case. Here we demonstrate dynamical control over this interaction by applying Floquet engineering to two superconducting qubits coupled to a waveguide terminated by a capacitive mirror. By positioning one qubit at an antinode and the other qubit at a node or an antinode of the resonant standing wave, we realize a Hermitian or non-Hermitian coupling between the two qubits. A periodic flux drive of the qubit frequencies then enables on-demand control of the coherent energy splitting and the collective decay. Our results establish Floquet engineering as a route to dynamically reshape both coherent and dissipative photon-mediated interactions between remote quantum emitters.