Beyond Strong Coupling in a Multimode Cavity

Here, we report an experimental realization of multimode strong coupling in cavity quantum electrodynamics. This novel regime is achieved when a single artificial atom is simultaneously strongly coupled to a large, but discrete, number of nondegenerate photonic modes of a cavity with coupling strengths comparable to the free spectral range. Our experiment reveals complex quantum multimode dynamics and spontaneous generation of quantum coherence, as evidenced by resonance fluorescence spanning many modes and ultranarrow linewidth emission. This work opens a new avenue for future experiments in light-matter interactions and poses a challenge to current theoretical approaches to its study.

Popular Summary

The theory of interacting light and matter has motivated much of the early development of quantum theory and has led to practical applications such as the laser. This field has seen a resurgence since the achievement of strong coupling between a single light mode and a single atom, which opened up the possibility of groundbreaking applications in quantum information processing, communication, and sensing. There is now a growing interest in exploring beyond strong coupling, a challenge we adopt in this work. The problem at hand is understanding the quantum states of a system with a large, but still discrete, number of degrees of freedom: work entering the realm of many-body physics with light.

We begin by coupling an artificial atom to a very long (about 0.68 m) superconducting cavity designed such that the coupling strength of the atom to high harmonics of the resonator approaches the spacing of the harmonic modes. We show that a very large number of light modes (about 50) can be simultaneously strongly coupled. In this situation, the artificial atom acts as an intermediary between the light modes. Remarkably, when we illuminate the cavity with microwaves, we observe the development of ultranarrow linewidths, which signals the spontaneous generation of quantum coherence; this constructive quantum interference in spontaneous decays of the system can be used to engineer its dissipation and decoherence. Our results show that linewidth narrowing occurs simultaneously and symmetrically across many modes and that the linewidths are inversely proportional to photon number, a combined phenomenon that has not been observed before.

Our work demonstrates a promising new direction for research in light-matter interactions and suggests possible applications to quantum-engineered systems.

Figure 1

Device for achieving MMSC. (a) A low fundamental frequency ${\omega }_0/2\pi \sim 92\mathrm{MHz}$ is realized by fabricating a meandering 0.68-m coplanar waveguide resonator on a $25\times 25\text{−}\mathrm{mm}$ sapphire substrate. The capacitive coupling at the input and output ports allows coupling of radiation into and out of the resonator, at rates ${\kappa }_m/2\pi \sim 0.5-3\mathrm{MHz}$. Red rectangles show coupling capacitors. The blue rectangle encloses the qubit. (b) Symmetric interdigitated capacitors define the cavity boundaries and couple radiation to the transmission lines. (c) A transmon qubit is capacitively coupled to the center pin near the output capacitor, an antinode for all modes. Superconducting quantum interference device geometry allows for tuning qubit frequency ${\omega }_a$ via the flux bias line (shown) or the external magnet [24]. The gridlike pattern in the ground plane pins flux vortices. Scale bars denote (a) 10 mm, (b) $100\mu \mathrm{m}$, and (c) $100\mu \mathrm{m}$.

Figure 2

Demonstrating multimode strong coupling. (a) Low power cavity transmission as qubit frequency is tuned with an applied flux bias. Vacuum Rabi avoided crossings are visible as the qubit is tuned into resonance with each mode (bright vertical lines spaced by approximately 92 MHz). It is apparent that the vacuum Rabi splitting is comparable with the free spectral range (mode spacing), thus indicating that MMSC has been achieved. White rectangles are shown in (b) and (c). The coupling $g_m$ grows with $\mathrm{m}:g_0\sqrt{m+1}$. (c) A single-mode fit of the splittings (white dashed line) is not accurate, as evidenced by the strongly shifted states near the central avoided crossing. A fit to the first manifold of the multimode Jaynes-Cummings incorporates all nearby polariton states, yielding $g_0\sim 3.75\mathrm{MHz}$.

Figure 3

Multimode resonance fluorescence. (a) Power spectrum for varying drive power $P_d$, when ${\omega }_d={\omega }_a={\omega }_{74}$, measured at more than 50 modes. Mode index $n$ is the relative detuning from the drive mode $n=m-74$. Power is measured in a 10-MHz window around each mode, excluding the driven mode ($n=0$). Increasing drive power unveils fluorescence at farther-detuned modes, strong emission from multiphoton processes, and complex multilobed fluorescence spectra. (b) The drive power corresponding to peak fluorescence for each far-detuned mode shows a quadratic dependence on detuning, suggesting this fluorescence is due to cavity-enhanced sideband fluorescence [9]. Modes near the drive frequency (see the inset) do not follow the quadratic fit due to strong multimode interaction. (c) Detailed plot of $n=-30$ from (a) shows a multilobed structure in fluorescence spectrum. Bare mode frequency is denoted with a vertical white line. For (d)–(g), ${\omega }_d={\omega }_a={\omega }_{68}$. (d) We explore the difference between the two lobes seen in (c) for several modes ($n=-36$, $-34$, $-32$, $-30$, $-28$, from bottom to top with individual curves vertically displaced for clarity) by measuring the total fluorescence power in a 6-MHz window while varying drive power. The drive powers corresponding to peak fluorescence move oppositely with mode number for the two lobes. (e)–(g) For modes near the drive ($n=-1,1,2$), strong multimode interaction further yields a more complex multilobed structure. Bare cavity-mode frequencies are denoted with vertical white lines.

Figure 4

Ultranarrowing of fluorescence. (a) Power spectrum ($n=1$) for varying drive frequency (${\omega }_d/2\pi$), at fixed drive power, reveals linewidth narrowing. Minimum linewidth 65 kHz corresponds to $({\omega }_d-{\omega }_{68})/2\pi =2\mathrm{MHz}$. (b) Normalized spectra along dashed lines in (a) are plotted in blue and vertically displaced. For comparison, low power transmission is plotted in solid gray lines and the bare mode frequency is denoted with a vertical gray line. (c) Emitted power (over approximately 3-MHz bandwidth) vs ${\omega }_d/2\pi$ shows simultaneous brightening of $n=\pm 1$ modes. (d) Fluorescence linewidths vs ${\omega }_d/2\pi$. Linewidths vary concurrently for $n=\pm 1$ and are inversely proportional to emitted power. For comparison, dashed lines show $\kappa /2\pi$.