Nonlinear response of the vacuum Rabi resonance

On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By employing a cavity to confine the field, the strength of this interaction can be increased many orders of magnitude to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics has been reached for real atoms in optical cavities, and for artificial atoms in circuit QED and quantum-dot systems. 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 QED 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 additional peaks with the characteristic sqrt(n) spacing of the Jaynes-Cummings ladder. These constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.Comment: 6 pages, 4 figures. Supplementary Material and Supplementary Movies are available at http://www.eng.yale.edu/rslab/publications.htm

Cooling a nanomechanical resonator with quantum back-action

Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radiofrequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latter's position;back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550mK to 300mK-- an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these backaction effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.Comment: 28 pages, 7 figures; accepted for publication in Natur

Quantum Non-demolition Detection of Single Microwave Photons in a Circuit

Thorough control of quantum measurement is key to the development of quantum information technologies. Many measurements are destructive, removing more information from the system than they obtain. Quantum non-demolition (QND) measurements allow repeated measurements that give the same eigenvalue. They could be used for several quantum information processing tasks such as error correction, preparation by measurement, and one-way quantum computing. Achieving QND measurements of photons is especially challenging because the detector must be completely transparent to the photons while still acquiring information about them. Recent progress in manipulating microwave photons in superconducting circuits has increased demand for a QND detector which operates in the gigahertz frequency range. Here we demonstrate a QND detection scheme which measures the number of photons inside a high quality-factor microwave cavity on a chip. This scheme maps a photon number onto a qubit state in a single-shot via qubit-photon logic gates. We verify the operation of the device by analyzing the average correlations of repeated measurements, and show that it is 90% QND. It differs from previously reported detectors because its sensitivity is strongly selective to chosen photon number states. This scheme could be used to monitor the state of a photon-based memory in a quantum computer.Comment: 5 pages, 4 figures, includes supplementary materia

Noiseless nonreciprocity in a parametric active device

Nonreciprocal devices such as circulators and isolators belong to an important class of microwave components employed in applications like the measurement of mesoscopic circuits at cryogenic temperatures. The measurement protocols usually involve an amplification chain which relies on circulators to separate input and output channels and to suppress backaction from different stages on the sample under test. In these devices the usual reciprocal symmetry of circuits is broken by the phenomenon of Faraday rotation based on magnetic materials and fields. However, magnets are averse to on-chip integration, and magnetic fields are deleterious to delicate superconducting devices. Here we present a new proposal combining two stages of parametric modulation emulating the action of a circulator. It is devoid of magnetic components and suitable for on-chip integration. As the design is free of any dissipative elements and based on reversible operation, the device operates noiselessly, giving it an important advantage over other nonreciprocal active devices for quantum information processing applications.Comment: 17 pages, 4 figures + 12 pages Supplementary Informatio

Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?

In cavity quantum electrodynamics (QED), the interaction between an atomic transition and the cavity field is measured by the vacuum Rabi frequency $\Omega_0$. The analogous term "circuit QED" has been introduced for Josephson junctions, because superconducting circuits behave as artificial atoms coupled to the bosonic field of a resonator. In the regime with $\Omega_0$ comparable to the two-level transition frequency, "superradiant" quantum phase transitions for the cavity vacuum have been predicted, e.g. within the Dicke model. Here, we prove that if the time-independent light-matter Hamiltonian is considered, a superradiant quantum critical point is forbidden for electric dipole atomic transitions due to the oscillator strength sum rule. In circuit QED, the capacitive coupling is analogous to the electric dipole one: yet, such no-go property can be circumvented by Cooper pair boxes capacitively coupled to a resonator, due to their peculiar Hilbert space topology and a violation of the corresponding sum rule

Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System

The already very active field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has recently gained additional momentum by the advent of experiments with semiconducting and superconducting systems. In these solid state implementations, novel quantum optics experiments are enabled by the possibility to engineer many of the characteristic parameters at will. In cavity QED, the observation of the vacuum Rabi mode splitting is a hallmark experiment aimed at probing the nature of matter-light interaction on the level of a single quantum. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous, long sought for spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED setup, in which ultra strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high quality on-chip microwave cavity.Comment: ArXiv version of manuscript published in Nature in July 2008, 5 pages, 5 figures, hi-res version at http://www.finkjohannes.com/SqrtNArxivPreprint.pd

Microcavity controlled coupling of excitonic qubits

Controlled non-local energy and coherence transfer enables light harvesting in photosynthesis and non-local logical operations in quantum computing. The most relevant mechanism of coherent coupling of distant qubits is coupling via the electromagnetic field. Here, we demonstrate the controlled coherent coupling of spatially separated excitonic qubits via the photon mode of a solid state microresonator. This is revealed by two-dimensional spectroscopy of the sample's coherent response, a sensitive and selective probe of the coherent coupling. The experimental results are quantitatively described by a rigorous theory of the cavity mediated coupling within a cluster of quantum dots excitons. Having demonstrated this mechanism, it can be used in extended coupling channels - sculptured, for instance, in photonic crystal cavities - to enable a long-range, non-local wiring up of individual emitters in solids

Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime

In cavity quantum electrodynamics (QED), 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, 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 and the cavity transition frequency above the percent level. While these experiments are well described by the renowned Jaynes-Cummings model, novel physics is expected in the ultrastrong coupling limit. 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.Comment: 5 pages, 3 figure

Current measurement by real-time counting of single electrons

The fact that electrical current is carried by individual charges has been known for over 100 years, yet this discreteness has not been directly observed so far. Almost all current measurements involve measuring the voltage drop across a resistor, using Ohm's law, in which the discrete nature of charge does not come into play. However, by sending a direct current through a microelectronic circuit with a chain of islands connected by small tunnel junctions, the individual electrons can be observed one by one. The quantum mechanical tunnelling of single charges in this one-dimensional array is time correlated, and consequently the detected signal has the average frequency f=I/e, where I is the current and e is the electron charge. Here we report a direct observation of these time-correlated single-electron tunnelling oscillations, and show electron counting in the range 5 fA-1 pA. This represents a fundamentally new way to measure extremely small currents, without offset or drift. Moreover, our current measurement, which is based on electron counting, is self-calibrated, as the measured frequency is related to the current only by a natural constant.Comment: 9 pages, 4 figures; v2: minor revisions, 2 refs added, words added to title, typos correcte

Coherent optical wavelength conversion via cavity-optomechanics

We theoretically propose and experimentally demonstrate coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system. For an engineered silicon optomechanical crystal nanocavity supporting a 4 GHz localized phonon mode, optical signals in a 1.5 MHz bandwidth are coherently converted over a 11.2 THz frequency span between one cavity mode at wavelength 1460 nm and a second cavity mode at 1545 nm with a 93% internal (2% external) peak efficiency. The thermal and quantum limiting noise involved in the conversion process is also analyzed, and in terms of an equivalent photon number signal level are found to correspond to an internal noise level of only 6 and 4x10-3 quanta, respectively.Comment: 11 pages, 7 figures, appendi