Strong coupling in a single quantum dot–semiconductor microcavity system

Reithmaier, Johann Peter; Sęk, G.; Löffler, Andreas; Hofmann, C.; Kuhn, S.; Reitzenstein, Stephan; Keldysh, L. V.; Kulakovskiĭ, V. D.; Reinecke, T. L.; Forchel, A.

doi:10.1038/nature02969

Cited by 1,916 publications

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“…By using a cavity to confine the field, the strength of this interaction can be increased by many orders of magnitude, to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics 1,2 has been reached for real atoms in optical cavities 3 , and for artificial atoms in circuit quantum electrodynamics 4 and quantum dot systems 5,6 . A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity, an effect known as vacuum Rabi splitting.…”

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confidence: 99%

Nonlinear response of the vacuum Rabi resonance

et al. 2008

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On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By using a cavity to confine the field, the strength of this interaction can be increased by many orders of magnitude, to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics 1,2 has been reached for real atoms in optical cavities 3 , and for artificial atoms in circuit quantum electrodynamics 4 and quantum dot systems 5,6 . A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity, an effect known as vacuum Rabi splitting. The circuit quantum electrodynamics architecture is ideally suited for going beyond this linear-response effect. Here, we show that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet and the appearance of extra peaks with the characteristic √ n spacing of the Jaynes-Cummings ladder. These findings constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.Circuit quantum electrodynamics (QED) realizes the coupling between a superconducting qubit and the microwave field inside an on-chip transmission-line resonator 4,7 . The drastic reduction in mode volume for such a quasi-one-dimensional system 8,9 , the recent improvement in coherence times 10 and the absence of atomic motion render circuit QED an ideal system for studying the strong-coupling limit. In the customary linear-response measurement of the transmitted microwave radiation, the vacuum Rabi splitting manifests itself as an avoided crossing between the qubit and the resonator.It may be argued that the observation of the splitting is not yet a clear sign for quantum behaviour 11,12 , because avoided crossings are also ubiquitous in classical physics. However, quantum mechanics gives rise to a distinct anharmonicity of these splittings when initializing the resonator in a higher photon Fock state: when the resonator mode is occupied by n photons, the splitting is enhanced by a factor √ n + 1 as compared with the vacuum Rabi situation. This anharmonicity has been observed with single atoms in both microwave 13 and optical cavities 14,15 . In circuit QED, this characteristic trait has been observed in time-domain measurements 16 . In a system similar to ours, the position of the n = 2 peaks was recently demonstrated in a two-tone pump-probe measurement 17 .Here, we present a theoretical analysis and experimental investigation of the vacuum Rabi resonance in a circuit QED system, where we study the √ n anharmonicity up to n = 5 by exploring the power dependence of the heterodyne transmission (see the Methods section). This type of detection is particularly simple, because it is a continuous measurement involving only a single dr...

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Nonlinear response of the vacuum Rabi resonance

et al. 2008

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“…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 .…”

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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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“…Currently also the optical control of QDs in a microcavity has come into the focus of attention, where vacuum Rabi oscillations and the corresponding vacuum Rabi splitting are seen as indications for reaching the strong coupling regime between light and matter [176,177,178,179]. In the case of strong light-matter coupling there is a strong interplay between exciton-phonon and light-matter interaction, which for example can be seen in the line-width broadening in the Mollow-Triplet [180,102].…”

Section: Rabi Rotationsmentioning

confidence: 99%

“…For dots without a cavity, this is not a very severe restriction, as the typical time scale for radiative decay is of the order of one nanosecond [78,79,80]. For dots in cavities, often cavity losses are the main relaxation process [176,213] which, depending on the quality factor, can demand for noticeably shorter preparation times.…”

Section: Phonon Assisted Exciton and Biexciton Preparationmentioning

confidence: 99%

The role of phonons for exciton and biexciton generation in an optically driven quantum dot

Reiter

Kuhn

Glässl

et al. 2014

J. Phys.: Condens. Matter

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Abstract. For many applications of semiconductor quantum dots in quantum technology a well controlled state preparation of the quantum dot states is mandatory. Since quantum dots are embedded in the semiconductor matrix, the interaction with phonons plays often a major role in the preparation process. In this review, we discuss the influence of phonons on three basically different optical excitation schemes which can be used for the preparation of exciton, biexciton, and superposition states: a resonant excitation leading to Rabi rotations in the excitonic system, an excitation with chirped pulses exploiting the effect of adiabatic rapid passage, and an off-resonant excitation giving rise to a phononassisted state preparation. We give an overview over experimental and theoretical results showing the role of the phonons and compare the performance of the schemes for state preparation.

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Strong coupling in a single quantum dot–semiconductor microcavity system

Cited by 1,916 publications

References 25 publications

Nonlinear response of the vacuum Rabi resonance

Nonlinear response of the vacuum Rabi resonance

Circuit quantum electrodynamics in the ultrastrong-coupling regime

The role of phonons for exciton and biexciton generation in an optically driven quantum dot

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