Black-Box Superconducting Circuit Quantization

Nigg, Simon E.; Paik, Hanhee; Vlastakis, Brian; Kirchmair, Gerhard; Shankar, Shyam; Frunzio, Luigi; Devoret, Michel; Schoelkopf, Robert; Girvin, S. M.

doi:10.1103/physrevlett.108.240502

Cited by 295 publications

(395 citation statements)

References 29 publications

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“…Another cut-off associated with the non-zero capacitance of the qubit to ground 23 leads to a similar shift. This issue can be overcome by using black-box circuit quantization, 36 but with this method we would lose the strict separation of atomic and photonic degrees of freedom typical of the Rabi model, which is essential to estimating the role of counter-rotating terms in the system's spectrum. Additionally, the analysis is then limited to the weakly anharmonic regime of the transmon qubit whilst our system also enters the Cooper-pair box regime (see Fig.…”

Section: Resultsmentioning

confidence: 99%

Multi-mode ultra-strong coupling in circuit quantum electrodynamics

et al. 2017

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With the introduction of superconducting circuits into the field of quantum optics, many experimental demonstrations of the quantum physics of an artificial atom coupled to a single-mode light field have been realized. Engineering such quantum systems offers the opportunity to explore extreme regimes of light-matter interaction that are inaccessible with natural systems. For instance the coupling strength g can be increased until it is comparable with the atomic or mode frequency ω a,m and the atom can be coupled to multiple modes which has always challenged our understanding of light-matter interaction. Here, we experimentally realize a transmon qubit in the ultra-strong coupling regime, reaching coupling ratios of g/ω m = 0.19 and we measure multi-mode interactions through a hybridization of the qubit up to the fifth mode of the resonator. This is enabled by a qubit with 88% of its capacitance formed by a vacuum-gap capacitance with the center conductor of a coplanar waveguide resonator. In addition to potential applications in quantum information technologies due to its small size, this architecture offers the potential to further explore the regime of multi-mode ultra-strong coupling. With strong coupling, 3 where the coupling is larger than the dissipation rates γ and κ of the atom and mode respectively, experiments such as photon-number resolution 4 or Schrödinger-cat revivals 5 have beautifully displayed the quantum physics of a single-atom coupled to the electromagnetic field of a single mode. As the field matures, circuits of larger complexity are explored, 6-8 opening the prospect of controllably studying systems that are theoretically and numerically difficult to understand.One example is the interaction between an (artificial) atom and an electromagnetic mode where the coupling rate becomes a considerable fraction of the atomic or mode eigen-frequency. This ultra-strong coupling (USC) regime, described by the quantum Rabi model, shows the breakdown of excitation number as conserved quantity, resulting in a significant theoretical challenge. 9,10 In the regime of g=ω a;m ' 1, known as deep-strong coupling (DSC), a symmetry breaking of the vacuum is predicted 11 (i.e., qualitative change of the ground state), similar to the Higgs mechanism or Jahn-Teller instability. To date, U/DSC with superconducting circuits has only been realized with flux qubits 6,12 or in the context of quantum simulations. 13,14 Using transmon qubits for USC is interesting due to their higher coherence rates 15 as well as their weakly-anharmonic nature, allowing the exploration of a different Hamiltonian than with flux qubits. 16 Since transmon qubits are currently a standard in quantum computing efforts, [17][18][19] implementing USC in a transmon architecture could also have technological applications by

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Section: Resultsmentioning

confidence: 99%

Multi-mode ultra-strong coupling in circuit quantum electrodynamics

et al. 2017

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“…An alternative for the global transmission resonator can be a resonator array [21,22,25,43], where we can use the common mode (k = 0) as the ancilla. Besides the above approach using capacitive coupling and JC interaction to generate the dispersive interaction perturbatively, one can also directly couple each resonator in the array to the qubits with a Josephson junction [48,49]. In this way, the dispersive interaction strength χ is only proportional to the Josephson energy E J and does not depend on the detuning in the form of g 2 a /∆ a , and hence can remain sizable even when the resonator and qubit is far detuned.…”

Section: A 2d Circuit-qed Networkmentioning

confidence: 99%

“…We define the detuning between qubits (σ j ) and coupling cavity bus (b) as ∆ b = − ω b . The last term in H 0 is the cross-Kerr interaction (with strength η) between the coupling (b) and ancilla (a) cavities, which can be experimentally realized, e.g., by coupling two superconducting cavities with a Josephson junction [48,49]. In the JC interaction term V, g j is the interaction strength between cavity and system qubits, which in general can depend on the qubits' locations and can also be disordered.…”

Section: A Non-local Modelmentioning

confidence: 99%

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Measurement of many-body chaos using a quantum clock

2016

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There has been recent progress in understanding chaotic features in many-body quantum systems. Motivated by the scrambling of information in black holes, it has been suggested that the time dependence of out-of-timeordered (OTO) correlation functions such as O 2 (t)O 1 (0)O 2 (t)O 1 (0) is a faithful measure of quantum chaos. Experimentally, these correlators are challenging to access since they apparently require access to both forward and backward time evolution with the system Hamiltonian. Here, we propose a protocol to measure such OTO correlators using an ancilla which controls the direction of time. Specifically, by coupling the state of ancilla to the system Hamiltonian of interest, we can emulate the forward and backward time propagation, where the ancilla plays the role of a 'quantum clock'. Within this scheme, the continuous evolution of the entire system (the system of interest and the ancilla) is governed by a time-independent Hamiltonian. Our protocol is immune to errors that could occur when the direction of time evolution is externally controlled by a classical switch.

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“…The most nonlinear oscillator in our circuit is the transmon whose nonlinearity originates from the Josephson junction with an inductance that is nonlinear with respect to the flux across it. This system is well described by the following Hamiltonian [25,29,35] …”

mentioning

confidence: 99%

Single-Photon-Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-Number States

et al. 2015

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Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying active feedback conditioned on an ancillary system or through reservoir engineering. Reservoir engineering maintains a desired quantum state through a combination of drives and designed entropy evacuation. We propose and implement a quantum reservoir engineering protocol that stabilizes Fock states in a microwave cavity. This protocol is realized with a circuit quantum electrodynamics platform where a Josephson junction provides direct, nonlinear coupling between two superconducting waveguide cavities. The nonlinear coupling results in a single photon resolved cross-Kerr effect between the two cavities enabling a photon number dependent coupling to a lossy environment. The quantum state of the microwave cavity is discussed in terms of a net polarization and is analyzed by a measurement of its steady state Wigner function.An unavoidable adversary in quantum information science is decoherence. A large scale quantum computer must implement error correction protocols to protect quantum states from decoherence [1]. A first step toward fault tolerant quantum error correction is the stabilization of a particular quantum state in the presence of decoherence [2]. One such implementation uses gate based architectures with measurement and feedback [3][4][5][6][7][8][9] for the correction of quantum errors. An alternative approach to active quantum systems is quantum-reservoir engineering (QRE) [10-13] which harnesses persistent, intentional coupling to the environment as a resource. Both cases require entropy removal yet only QRE employs environmental losses as a crucial part of their protocols. QRE does not require an external feedback with calculation since the Hamiltonian interactions are designed a priori to determine the final state avoiding uncertainty induced by the quantum-classical interface. In addition, QRE is less susceptible to experimental noise [14] and in some cases thrives in a noisy environment [15].QRE has been demonstrated in macroscopic atomic ensembles [16], trapped atomic systems [17], and superconducting circuits [18][19][20]. Circuit quantum electrodynamics (cQED) systems are an attractive platform for QRE due to the experimental freedom to design strong interactions between superconducting qubits and microwave cavities [21]. Interactions between a superconducting transmon qubit and a microwave cavity have demonstrated qubit-photon entanglement [21], creation of quantum oscillator states [22,23], and quantum nondemolition measurements of an oscillator [24]. Investigations using three dimensional waveguide cavities resulted in increased coherence times [25][26][27] In this Letter, we demonstrate the single photon resolved cross-Kerr effect between two superconducting microwave cavities which is a new regime of cQED. This nonlinear coupling causes an excitation in one cavity to change the resonance frequency of the other cavity by more than their combined linewidth. While the state dependent shi...

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Black-Box Superconducting Circuit Quantization

Cited by 295 publications

References 29 publications

Multi-mode ultra-strong coupling in circuit quantum electrodynamics

Multi-mode ultra-strong coupling in circuit quantum electrodynamics

Measurement of many-body chaos using a quantum clock

Single-Photon-Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-Number States

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