[Paper Review] In-situ frequency tuning of photons stored in a high Q microwave cavity

Martin Sandberg, C. M. Wilson+5 more|ArXiv.org|Jan 16, 2008

Photonic and Optical Devices1 references3 citations

TL;DR

This paper demonstrates in-situ, ultrafast frequency tuning of individual microwave photons stored in a high-Q superconducting coplanar waveguide resonator by dynamically modulating a SQUID-based Josephson inductance. The device achieves detuning of over 330 MHz in less than 10 ns—faster than the cavity's photon lifetime—enabling coherent manipulation of individual photon frequencies, with key implications for dynamic qubit coupling in circuit quantum electrodynamics.

ABSTRACT

Photons are fundamental excitations of the electromagnetic field and can be captured in cavities. For a given cavity with a certain size, the fundamental mode has a fixed frequency f which gives the photons a specific "colour". The cavity also has a typical lifetime tau, which results in a finite linewidth delta f}. If the size of the cavity is changed fast compared to tau, and so that the frequency change Delta f >> delta f, then it is possible to change the "colour" of the captured photons. Here we demonstrate superconducting microwave cavities, with tunable effective lengths. The tuning is obtained by varying a Josephson inductance at one end of the cavity. We show tuning by several hundred linewidths in a time Delta t << tau. Working in the few photon limit, we show that photons stored in the cavity at one frequency will leak out from the cavity with the new frequency after the detuning. The characteristics of the measured devices make them suitable for dynamic coupling of qubits.

Motivation & Objective

• To develop a tunable superconducting microwave cavity capable of fast, in-situ frequency control for dynamic quantum operations.
• To address the challenge of maintaining qubit coherence during coupling by enabling resonator-based qubit interaction instead of qubit tuning.
• To demonstrate that individual photons can be frequency-tuned in the few-photon regime, confirming coherent photon energy manipulation.
• To achieve high tunability range and speed while preserving high internal quality factor (Q) for long photon storage times.
• To enable a new platform for dynamic coupling of superconducting qubits and for studying nonclassical photon states.

Proposed method

• A quarter-wavelength superconducting coplanar waveguide (CPW) resonator is fabricated on a sapphire substrate with a 400 nm thermal SiO2 layer.
• One end of the resonator is terminated with one or more SQUIDs in series, which act as tunable inductors via magnetic flux control.
• The SQUID inductance is modeled using the nonlinear inductance equation $ L_s = \frac{\Phi_0}{4\pi I_c |\cos(\pi\Phi/\Phi_0)|} \sqrt{1 - \left(\frac{I}{2I_c \cos(\pi\Phi/\Phi_0)}\right)^2} $, enabling dynamic frequency tuning.
• The resonator is probed using microwave reflectometry with a drive signal, and the reflection coefficient $ \Gamma = \frac{V_r}{V_d} $ is measured via scattering matrix formalism.
• Fast flux pulses (as short as 10 ns, rise time ~3 ns) are applied to the SQUID to rapidly detune the cavity frequency, with the system's response measured in real time.
• The system is operated at 20 mK to minimize thermal photon occupation, ensuring the few-photon regime is accessible.

Experimental results

Research questions

• RQ1 Can the frequency of individual microwave photons stored in a high-Q cavity be tuned in real time without destroying their coherence?
• RQ2 What is the minimum timescale for frequency detuning that still allows coherent photon energy transfer during the tuning process?
• RQ3 To what extent can the resonator frequency be detuned while maintaining high quality factor and low dissipation?
• RQ4 Can the tuning mechanism be used to coherently compress or stretch stored photons, effectively changing their energy?
• RQ5 How does the speed of tuning compare to the cavity's photon lifetime, and what are the implications for dynamic quantum control?

Key findings

• The device achieves a frequency detuning of up to 700 MHz in a 4.9 GHz resonator, exceeding 250 linewidths, demonstrating a large tuning range.
• A 330 MHz detuning was achieved in a 10 ns pulse with a rise time of only 3 ns, confirming tuning speeds far exceeding the cavity's photon lifetime.
• The system maintains a high internal Q factor, with measured Q values close to theoretical expectations, despite minor degradation due to pulse amplitude jitter.
• In the few-photon regime (average photon number ~5), the photons are observed to adjust to the new cavity frequency after detuning, confirming coherent frequency tuning of individual photons.
• The device supports both increasing and decreasing the resonant frequency via fast flux pulses, enabling bidirectional tuning of stored photon energy.
• Multiple reflections from imperfect pulse lines were observed, but the core fast oscillations confirm that the tuning dynamics are well-resolved at the nanosecond scale.