Synthesizing arbitrary quantum states in a superconducting resonator

Hofheinz, M.; Wang, H.; Ansmann, M.; Bialczak, Radoslaw C.; Lucero, Erik; Neeley, M.; O’Connell, A. D.; Sank, D.; Wenner, J.; Martinis, John M.; Cleland, A. N.

doi:10.1038/nature08005

Cited by 833 publications

(953 citation statements)

References 28 publications

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“…At the static flux bias DC = 0.37 0 , indicated in Fig. 1(b), we find ω 3 /2π = 4.345 GHz, ω 4 /2π = 6.150 GHz, 30 /2π = 0.52 MHz, 3 /2π = 0.56 MHz, 40 /2π = 0.70 MHz, and 4 /2π = 0.78 MHz. The Kerr coefficients are determined from properties of the parametric oscillations and explained later.…”

Section: Experimental Methodsmentioning

confidence: 91%

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Nondegenerate parametric oscillations in a tunable superconducting resonator

et al. 2018

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We investigate nondegenerate parametric oscillations in a superconducting microwave multimode resonator that is terminated by a superconducting quantum interference device (SQUID). The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonant tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.

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Section: Experimental Methodsmentioning

confidence: 91%

“…Within cQED, a variety of nonclassical photonic states can be efficiently generated by nonlinear superconducting elements: superpositions of Fock states [3], entangled two-mode photonic states [4][5][6], and multiphoton Schrödinger cat states [7]. Parametric phenomena have played important roles in this development.…”

Section: Introductionmentioning

confidence: 99%

Nondegenerate parametric oscillations in a tunable superconducting resonator

et al. 2018

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“…Qubits separated by relatively large distances have been coherently coupled using a cavity bus [4,5]. Finally, cQED enables the generation of classical and nonclassical light [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Double Quantum Dot Floquet Gain Medium

et al. 2016

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Strongly driving a two-level quantum system with light leads to a ladder of Floquet states separated by the photon energy. Nanoscale quantum devices allow the interplay of confined electrons, phonons, and photons to be studied under strong driving conditions. Here, we show that a single electron in a periodically driven double quantum dot functions as a "Floquet gain medium," where population imbalances in the double quantum dot Floquet quasienergy levels lead to an intricate pattern of gain and loss features in the cavity response. We further measure a large intracavity photon number n c in the absence of a cavity drive field, due to equilibration in the Floquet picture. Our device operates in the absence of a dc current-one and the same electron is repeatedly driven to the excited state to generate population inversion. These results pave the way to future studies of nonclassical light and thermalization of driven quantum systems.

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“…This unique possibility to experimentally explore the foundations of quantum physics has greatly evolved with the advent of circuit QED [4][5][6][7][8][9][10][11][12][13] , where on-chip superconducting qubits and oscillators play the roles of two-level atoms and cavities, respectively. In the strong coupling limit, atom and cavity can exchange a photon frequently before coherence is lost.…”

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confidence: 99%

Circuit quantum electrodynamics in the ultrastrong-coupling regime

et al. 2010

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In cavity quantum electrodynamics (QED) 1-3 , light-matter interaction is probed at its most fundamental level, where individual atoms are coupled to single photons stored in three-dimensional cavities. This unique possibility to experimentally explore the foundations of quantum physics has greatly evolved with the advent of circuit QED 4-13 , where on-chip superconducting qubits and oscillators play the roles of two-level atoms and cavities, respectively. In the strong coupling limit, atom and cavity can exchange a photon frequently before coherence is lost. This important regime has been reached both in cavity and circuit QED, but the design flexibility and engineering potential of the latter allowed for increasing the ratio between the atom-cavity coupling rate g and the cavity transition frequency ωr above the percent level 8,14,15 . While these experiments are well described by the renowned Jaynes-Cummings model 16 , novel physics is expected when g reaches a considerable fraction of ωr. Promising steps towards this so-called ultrastrong coupling regime 17,18 have recently been taken in semiconductor structures 19,20 . Here, we report on the first experimental realization of a superconducting circuit QED system in the ultrastrong coupling limit and present direct evidence for the breakdown of the Jaynes-Cummings model. We reach remarkable normalized coupling rates g/ωr of up to 12 % by enhancing the inductive coupling of a flux qubit 21 to a transmission line resonator using the nonlinear inductance of a Josephson junction 22 . Our circuit extends the toolbox of quantum optics on a chip towards exciting explorations of the ultrastrong interaction between light and matter.In the strong coupling regime, the atom-cavity coupling rate g exceeds the dissipation rates κ and γ of both, cavity and atom, giving rise to coherent light-matter oscillations and superposition states. This regime was reached in various types of systems operating at different energy scales [1][2][3][23][24][25] . At microwave frequencies, strong coupling is feasible due to the enormous engineerability of superconducting circuit QED systems 4,5 . Here, small cavity mode volumes and large dipole moments of artificial atoms 26 enable coupling rates g of about 15 1 % of the cavity mode frequency ω r . Nevertheless, as in cavity QED, the quantum dynamics of these systems follows the Jaynes-Cummings model, which describes the coherent exchange of a single excitation between the atom and the cavity mode. Although the Hamiltonian of a realistic atom-cavity system contains so-called counterrotating terms allowing the simultaneous creation ior annihilation of an excitation in both atom and cavity mode, these terms can be safely neglected for small normalized coupling rates g/ω r . However, when g becomes a significant fraction of ω r , the counterrotating terms are expected to manifest, giving rise to exciting effects in QED.The ultrastrong coupling regime is difficult to reach in traditional quantum optics, but was recently realized in a solid-stat...

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Synthesizing arbitrary quantum states in a superconducting resonator

Cited by 833 publications

References 28 publications

Nondegenerate parametric oscillations in a tunable superconducting resonator

Nondegenerate parametric oscillations in a tunable superconducting resonator

Double Quantum Dot Floquet Gain Medium

Circuit quantum electrodynamics in the ultrastrong-coupling regime

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