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Probing the Tavis-Cummings level splitting with intermediate-scale superconducting circuits

Yang, P., Brehm, J., Leppäkangas, J., Guo, L., Marthaler, M., Isabella Boventer, Stehli, A., Wolz, T., Ustinov, A., Weides, M.

Published Aug 11, 2020• 10 citations
OpenAlex

Abstract

We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, being the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator's attainable size of dressed states is limited by reduced signal visibility, and -if uncalibrated- by off-resonance shifts of sub-components. Our work demonstrates control and readout of quantum coherent mesoscopic multi-qubit system of intermediate scale under conditions of noise.

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We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, which is the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator's attainable size of dressed states with up to five qubits is limited by reduced signal visibility, and---if uncalibrated---by off-resonance shifts of subcomponents. Our work demonstrates control and readout of a quantum coherent mesoscopic multiqubit system of intermediate scale under conditions of noise.

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The Tavis-Cummings model is intensively investigated in quantum optics and has important applications in generation of multi-atom entanglement. Here, we employ a superconducting circuit quantum electrodynamic system to study a modified Tavis-Cummings model with directly-coupled atoms. In our device, three superconducting artificial atoms are arranged in a chain with direct coupling through fixed capacitors and strongly coupled to a transmission line resonator. By performing transmission spectrum measurements, we observe different anticrossing structures when one or two qubits are resonantly coupled to the resonator. In the case of the two-qubit Tavis-Cummings model without qubit-qubit interaction, we observe two dips at the resonance point of the anticrossing. The splitting of these dips is determined by Δ λ =2 g 1 2 + g 3 2 , where g 1 and g 3 are the coupling strengths between Qubit 1 and the resonator, and Qubit 3 and the resonator, respectively. The direct coupling J 12 between the two qubits results in three dressed states in the two-qubit Tavis-Cummings model at the frequency resonance point, leading to three dips in the transmission spectrum. In this case, the distance between the two farthest and asymmetrical dips, arising from the energy level splitting, is larger than in the previous case. The frequency interval between these two dips is determined by the difference in eigenvalues (Δ λ = ε 1+ − ε 1− ), obtained through numerical calculations. What we believe as novel and intriguing experimental results may potentially advance quantum optics experiments, providing valuable insights for future research.

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Nonlinearities in the strong coupling regime of the Tavis-Cummings model: from multi-photon resonances to bistability

András Dombi, András Vukics, P. Domokos

In the strong coupling regime of cavity QED where the characteristic damping rates are orders of magnitude below the coherent coupling, resolved multi-photon resonances can be observed for strong enough driving strength. In a certain frequency range, the external coherent drive field hits multi-photon resonances which correspond to very high order transitions that cannot be excited at the given power of the driving field. We found that in this range the cavity field evolves into a robust semiclassical solution which is the mixture of the vacuum and an excited quasi-classical state. The system is reminiscent of optical bistability, however, here a single atom produces a telegraph signal for the outgoing intensity by switching between two states with large photon number difference. We calculate this behavior also for the Tavis-Cummings model representing three qubits in an existing circuit QED experimental setting.

•Apr 30, 2014•0 citations
We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, being the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator's attainable size of dressed states is limited by reduced signal visibility, and -if uncalibrated- by off-resonance shifts of sub-components. Our work demonstrates control and readout of quantum coherent mesoscopic multi-qubit system of intermediate scale under conditions of noise.
We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system (qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, which is the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator's attainable size of dressed states with up to five qubits is limited by reduced signal visibility, and---if uncalibrated---by off-resonance shifts of subcomponents. Our work demonstrates control and readout of a quantum coherent mesoscopic multiqubit system of intermediate scale under conditions of noise.
We present an ideal realization of the Tavis-Cummings model in the absence of atom number and coupling fluctuations by embedding a discrete number of fully controllable superconducting qubits at fixed positions into a transmission line resonator. Measuring the vacuum Rabi mode splitting with one, two, and three qubits strongly coupled to the cavity field, we explore both bright and dark dressed collective multiqubit states and observe the discrete square root N scaling of the collective dipole coupling strength. Our experiments demonstrate a novel approach to explore collective states, such as the W state, in a fully globally and locally controllable quantum system. Our scalable approach is interesting for solid-state quantum information processing and for fundamental multiatom quantum optics experiments with fixed atom numbers.
We explore experimentally a quantum metamaterial based on a superconducting chip with 25 frequency-tunable transmon qubits coupled to a common coplanar resonator. The collective bright and dark modes are probed via the microwave response, i.e., by measuring the transmission amplitude of an external microwave signal. All qubits have individual control and readout lines. Their frequency tunability allows the number NNN of resonantly coupled qubits to change and a disorder in their excitation frequencies to be introduced with preassigned distributions. While increasing NNN, we demonstrate the expected N1/2{N}^{1/2}N1/2 scaling law for the energy gap (Rabi splitting) between bright modes around the cavity frequency. By introducing a controllable disorder and averaging the transmission amplitude over a large number of realizations, we demonstrate a decay of mesoscopic fluctuations which mimics an approach towards the thermodynamic limit. The collective bright states survive in the presence of disorder when the strength of individual qubit coupling to the cavity dominates over the disorder strength.
The Tavis-Cummings model is intensively investigated in quantum optics and has important applications in generation of multi-atom entanglement. Here, we employ a superconducting circuit quantum electrodynamic system to study a modified Tavis-Cummings model with directly-coupled atoms. In our device, three superconducting artificial atoms are arranged in a chain with direct coupling through fixed capacitors and strongly coupled to a transmission line resonator. By performing transmission spectrum measurements, we observe different anticrossing structures when one or two qubits are resonantly coupled to the resonator. In the case of the two-qubit Tavis-Cummings model without qubit-qubit interaction, we observe two dips at the resonance point of the anticrossing. The splitting of these dips is determined by Δ λ =2 g 1 2 + g 3 2 , where g 1 and g 3 are the coupling strengths between Qubit 1 and the resonator, and Qubit 3 and the resonator, respectively. The direct coupling J 12 between the two qubits results in three dressed states in the two-qubit Tavis-Cummings model at the frequency resonance point, leading to three dips in the transmission spectrum. In this case, the distance between the two farthest and asymmetrical dips, arising from the energy level splitting, is larger than in the previous case. The frequency interval between these two dips is determined by the difference in eigenvalues (Δ λ = ε 1+ − ε 1− ), obtained through numerical calculations. What we believe as novel and intriguing experimental results may potentially advance quantum optics experiments, providing valuable insights for future research.
Microscopic two-level systems (TLS) -- ubiquitous atomic-scale defects in solid-state quantum devices -- are a dominant source of qubit decoherence, yet their role is often considered local and short-memoried. Here, we report the observation of a coherent TLS that couples simultaneously to two spatially distant superconducting qubits. The TLS is identified to reside within the tunable coupler linking the qubits, enabling controllability of the TLS-qubit coupling strength via coupler frequency -- a capability absent in earlier studies. This tunability allows us to systematically probe how TLS distorts qubit dynamics, revisiting the decoherence model in the presence of non-Markovian TLS dephasing noise. This is corroborated by the reconstructed 1/f1/f1/f noise spectrum of TLS frequency fluctuation spanning more than ten orders of magnitude (0.1\,mHz -- 1\,MHz) that reveals discrete fluctuator signatures. Quantum process tomography further unveils TLS-induced correlated qubit dynamics, highlighting the long-lived TLS as an effective source of non-Markovianity. Our findings expose a previously overlooked interaction mechanism in scalable quantum architectures: defects embedded in coupling elements can simultaneously affect multiple qubits with variable impact. Beyond immediate implications for system characterization and calibration, this situation provides a powerful testbed for studying defect-driven quantum dynamics, refining error suppression strategies, and advancing architecture design for scalable quantum technologies.
In the strong coupling regime of cavity QED where the characteristic damping rates are orders of magnitude below the coherent coupling, resolved multi-photon resonances can be observed for strong enough driving strength. In a certain frequency range, the external coherent drive field hits multi-photon resonances which correspond to very high order transitions that cannot be excited at the given power of the driving field. We found that in this range the cavity field evolves into a robust semiclassical solution which is the mixture of the vacuum and an excited quasi-classical state. The system is reminiscent of optical bistability, however, here a single atom produces a telegraph signal for the outgoing intensity by switching between two states with large photon number difference. We calculate this behavior also for the Tavis-Cummings model representing three qubits in an existing circuit QED experimental setting.