Ultimate on-chip quantum amplifier

Single-photon switches, beam splitters, and circulators based on the photonic Aharonov-Bohm effect

Single-photon devices such as switches, beam splitters, and circulators are fundamental components to construct photonic integrated quantum networks. In this paper, two V-type three-level atoms coupled to a waveguide are proposed to simultaneously realize these functions as a multifunctional and reconfigurable single-photon device. When both the two atoms are driven by the external coherent fields, the difference in the phases of the coherent driving induces the photonic Aharonov-Bohm effect. Based on the photonic Aharonov-Bohm effect and setting the two-atom distance to match the constructive or destructive interference conditions among photons travelling along different paths, a single-photon switch is achieved since the incident single photon can be controlled from complete transmission to complete reflection by adjusting the amplitudes and phases of the driving fields. When properly changing the amplitudes and phases of the driving fields, the incident photons are split equally into multiple components as a beam splitter operated with different frequencies. Meanwhile, the single-photon circulator with reconfigurable circulation directions can also be obtained.

Circuit quantum electrodynamics with dressed states of a superconducting artificial atom

A dynamical control of the coupling strengths between dressed states and probe photon states is demonstrated with a transmon-like artificial atom coupled to two closely spaced resonant modes. When the atom is driven with one mode, the atom state and driving photon states form the so-called dressed states. Dressed states with sideband index up to 3 were prepared and probed via the strong coupling to the other resonant mode. Spectroscopy reveals that the coupling strengths are "dressed" and can be modulated by the power and sideband index of the driving. The transmission of the probe tone is modulated by the driving microwave amplitude with a Bessel behavior, displaying multi-photon process associated with the inter-atomic level transitions.

Two-photon scattering and correlation in a four-terminal waveguide system

Scattering and correlation properties of a two-photon (TP) pulse are studied in a four-terminal waveguide system, i.e., two one-dimensional waveguides connected by a Jaynes-Cummings emitter (JCE). The wave function approach is utilized to exactly calculate the real-time dynamic evolution of the TP transport. When the width of the incident TP Gaussian pulse is much larger than the photon wavelength, the TP transmission spectra approach that of the corresponding single photon cases and are almost independent of the pulse width. On the contrary, as the pulse width is comparable to the photon wavelength, the TP transmission and correlation both show strong dependence on the pulse width. The resonant scattering due to the JCE and the photon interference together determine the TP correlation. When the distance between the TPs is small, the TP correlations between any two terminals for the scattered TP pulse are much different from those for the incident TP pulse and therefore, such a four-terminal waveguide system provides a way to control the TP correlation.

Optical amplification assisted by two-photon processes in a 3-level transmon artificial atom

We experimentally study interactions between two microwave fields mediated by 3-level transmon artificial atom with two-photon processes. The transmon has good selection rule, preventing one-photon transition, but allowing two-photon transition from ground state(0) to 2nd excited state(2). By pumping a control tone in resonance to the transition between 1st(1) and 2nd excited state(2), we control the one-photon transparency for 0 to 1 transition and two-photon transparency for 0 to 2 transition. The results are explained by the Autler-Townes splitting induced by the control microwave. In addition, two possible microwave amplification processes involving two-photon processes are also studied. The 4-wave mixing scheme increases the transmission by 3% while 2-photon optical pumping produces a 11% narrowband increment. All these phenomena can be operated with control and probe tones in a narrow band.

Large Collective Lamb Shift of Two Distant Superconducting Artificial Atoms

Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift reaching 0.8% of the qubit transition frequency and twice the transition linewidth. We also show that the qubits can interact via the transmission line even if one of them does not decay into it.

Relativistic quantum heat engine from uncertainty relation standpoint

Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classical nature. For a concrete interpretation about the relation between the quantum observables with the physically measurable parameters (like the efficiency and work done), we develop a link between the thermodynamic variables and the uncertainty relation. We have used this model to explore the work extraction and the efficiency of the heat engine for a relativistic case from the standpoint of uncertainty relation, where the incompatible observables are the position and the momentum operators. We are able to determine the bounds (the upper and the lower bounds) of the efficiency of the heat engine through the thermal uncertainty relation.

Decoherence-Free Interaction between Giant Atoms in Waveguide Quantum Electrodynamics

In quantum-optics experiments with both natural and artificial atoms, the atoms are usually small enough that they can be approximated as pointlike compared to the wavelength of the electromagnetic radiation with which they interact. However, superconducting qubits coupled to a meandering transmission line, or to surface acoustic waves, can realize "giant artificial atoms" that couple to a bosonic field at several points which are wavelengths apart. Here, we study setups with multiple giant atoms coupled at multiple points to a one-dimensional (1D) waveguide. We show that the giant atoms can be protected from decohering through the waveguide, but still have exchange interactions mediated by the waveguide. Unlike in decoherence-free subspaces, here the entire multiatom Hilbert space (2^{N} states for N atoms) is protected from decoherence. This is not possible with "small" atoms. We further show how this decoherence-free interaction can be designed in setups with multiple atoms to implement, e.g., a 1D chain of atoms with nearest-neighbor couplings or a collection of atoms with all-to-all connectivity. This may have important applications in quantum simulation and quantum computing.

Reflective Amplification without Population Inversion from a Strongly Driven Superconducting Qubit

Amplification of optical or microwave fields is often achieved by strongly driving a medium to induce population inversion such that a weak probe can be amplified through stimulated emission. Here we strongly couple a superconducting qubit, an artificial atom, to the field in a semi-infinite waveguide. When driving the qubit strongly on resonance such that a Mollow triplet appears, we observe a 7% amplitude gain for a weak probe at frequencies in between the triplet. This amplification is not due to population inversion, neither in the bare qubit basis nor in the dressed-state basis, but instead results from a four-photon process that converts energy from the strong drive to the weak probe. We find excellent agreement between the experimental results and numerical simulations without any free fitting parameters. Since our device consists of a single two-level artificial atom, the simplest possible quantum system, it can be viewed as the most fundamental version of a four-wave-mixing parametric amplifier.

Quantum wave mixing and visualisation of coherent and superposed photonic states in a waveguide

Superconducting quantum systems (artificial atoms) have been recently successfully used to demonstrate on-chip effects of quantum optics with single atoms in the microwave range. In particular, a well-known effect of four wave mixing could reveal a series of features beyond classical physics, when a non-linear medium is scaled down to a single quantum scatterer. Here we demonstrate the phenomenon of quantum wave mixing (QWM) on a single superconducting artificial atom. In the QWM, the spectrum of elastically scattered radiation is a direct map of the interacting superposed and coherent photonic states. Moreover, the artificial atom visualises photon-state statistics, distinguishing coherent, one- and two-photon superposed states with the finite (quantised) number of peaks in the quantum regime. Our results may give a new insight into nonlinear quantum effects in microwave optics with artificial atoms.

The phenomenon of wave mixing is expected to show peculiar features when scaled down to the quantum level. Here, the authors show how coherent electromagnetic waves propagating in a 1D transmission line with an embedded two-level artificial atom are mapped into a quantised spectrum of narrow peaks.

Threshold Dynamics of a Semiconductor Single Atom Maser

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

Dynamic Stark shift induced by a single photon packet

The dynamic Stark shift results from the interaction of an atom with the electromagnetic field. We show how a propagating single-photon wave packet can induce a time-dependent dynamical Stark shift on a two-level system (TLS). A non-perturbative fully quantum treatment is employed, where the quantum dynamics of both the field and the TLS are analyzed. We also provide the means to experimentally access such time-dependent frequency by measuring the interference pattern in the electromagnetic field inside a 1D waveguide. The effect we evidence here may find applications in the autonomous quantum control of quantum systems without classical external fields, which can be useful for quantum information processing as well as for quantum thermodynamical tasks.

Quantum thermal diode based on two interacting spinlike systems under different excitations

We demonstrate that two interacting spinlike systems characterized by different excitation frequencies and coupled to a thermal bath each, can be used as a quantum thermal diode capable of efficiently rectifying the heat current. This is done by deriving analytical expressions for both the heat current and rectification factor of the diode, based on the solution of a master equation for the density matrix. Higher rectification factors are obtained for lower heat currents, whose magnitude takes their maximum values for a given interaction coupling proportional to the temperature of the hotter thermal bath. It is shown that the rectification ability of the diode increases with the excitation frequencies difference, which drives the asymmetry of the heat current, when the temperatures of the thermal baths are inverted. Furthermore, explicit conditions for the optimization of the rectification factor and heat current are explicitly found.

Quantum Thermal Transistor

We demonstrate that a thermal transistor can be made up with a quantum system of three interacting subsystems, coupled to a thermal reservoir each. This thermal transistor is analogous to an electronic bipolar one with the ability to control the thermal currents at the collector and at the emitter with the imposed thermal current at the base. This is achieved by determining the heat fluxes by means of the strong-coupling formalism. For the case of three interacting spins, in which one of them is coupled to the other two, that are not directly coupled, it is shown that high amplification can be obtained in a wide range of energy parameters and temperatures. The proposed quantum transistor could, in principle, be used to develop devices such as a thermal modulator and a thermal amplifier in nanosystems.

Single photon transport along a one-dimensional waveguide with a side manipulated cavity QED system

An external mirror coupling to a cavity with a two-level atom inside is put forward to control the photon transport along a one-dimensional waveguide. Using a full quantum theory of photon transport in real space, it is shown that the Rabi splittings of the photonic transmission spectra can be controlled by the cavity-mirror couplings; the splittings could still be observed even when the cavity-atom system works in the weak coupling regime, and the transmission probability of the resonant photon can be modulated from 0 to 100%. Additionally, our numerical results show that the appearance of Fano resonance is related to the strengths of the cavity-mirror coupling and the dissipations of the system. An experimental demonstration of the proposal with the current photonic crystal waveguide technique is suggested.

Optimal rectification in the ultrastrong coupling regime

We study the effect of ultrastrong coupling on the transport of heat. In particular, we present a condition for optimal rectification, i.e., flow of heat in one direction and complete isolation in the opposite direction. We show that the strong-coupling formalism is necessary for correctly describing heat flow in a wide range of parameters, including moderate to low couplings. We present a situation in which the strong-coupling formalism predicts optimal rectification whereas the phenomenological approach predicts no heat flow in any direction, for the same parameter values.

Single-photon quantum router with multiple output ports

The routing capability is a requisite in quantum network. Although the quantum routing of signals has been investigated in various systems both in theory and experiment, the general form of quantum routing with many output terminals still needs to be explored. Here we propose a scheme to achieve the multi-channel quantum routing of the single photons in a waveguide-emitter system. The channels are composed by the waveguides and are connected by intermediate two-level emitters. By adjusting the intermediate emitters, the output channels of the input single photons can be controlled. This is demonstrated in the cases of one output channel, two output channels and the generic N output channels. The results show that the multi-channel quantum routing of single photons can be well achieved in the proposed system. This offers a scheme for the experimental realization of general quantum routing of single photons.

Waveguide-QED-based photonic quantum computation

We propose a new scheme for quantum computation using flying qubits--propagating photons in a one-dimensional waveguide interacting with matter qubits. Photon-photon interactions are mediated by the coupling to a four-level system, based on which photon-photon π-phase gates (CONTROLLED-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible, given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.

Observation of the three-state dressed states in circuit quantum electrodynamics

We have investigated the microwave response of a transmon qubit coupled directly to a transmission line. In a transmon qubit, owing to its weak anharmonicity, a single driving field may generate dressed states involving more than two bare states. We confirmed the formation of three-state dressed states by observing all of the six associated Rabi sidebands, which appear as either amplification or attenuation of the probe field. The experimental results are reproduced with good precision by a theoretical model incorporating the radiative coupling between the qubit and the microwave.

Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions

We study photon-photon correlations and entanglement generation in a one-dimensional waveguide coupled to two qubits with an arbitrary spatial separation. To treat the combination of nonlinear elements and 1D continuum, we develop a novel Green function method. The vacuum-mediated qubit-qubit interactions cause quantum beats to appear in the second-order correlation function. We go beyond the Markovian regime and observe that such quantum beats persist much longer than the qubit lifetime. A high degree of long-distance entanglement can be generated, increasing the potential of waveguide-QED systems for scalable quantum networking.

Dressed-state amplification by a single superconducting qubit

We demonstrate amplification of a microwave signal by a strongly driven two-level system in a coplanar waveguide resonator. The effect, similar to the dressed-state lasing known from quantum optics, is observed with a single quantum system formed by a persistent current (flux) qubit. The transmission through the resonator is enhanced when the Rabi frequency of the driven qubit is tuned into resonance with one of the resonator modes. Amplification as well as linewidth narrowing of a weak probe signal has been observed. The stimulated emission in the resonator has been studied by measuring the emission spectrum. We analyzed our system and found an excellent agreement between the experimental results and the theoretical predictions obtained in the dressed-state model.

Dynamical Autler-Townes control of a phase qubit

Routers, switches, and repeaters are essential components of modern information-processing systems. Similar devices will be needed in future superconducting quantum computers. In this work we investigate experimentally the time evolution of Autler-Townes splitting in a superconducting phase qubit under the application of a control tone resonantly coupled to the second transition. A three-level model that includes independently determined parameters for relaxation and dephasing gives excellent agreement with the experiment. The results demonstrate that the qubit can be used as a ON/OFF switch with 100 ns operating time-scale for the reflection/transmission of photons coming from an applied probe microwave tone. The ON state is realized when the control tone is sufficiently strong to generate an Autler-Townes doublet, suppressing the absorption of the probe tone photons and resulting in a maximum of transmission.

Stimulated emission from a single excited atom in a waveguide

We study stimulated emission from an excited two-level atom coupled to a waveguide containing an incident single-photon pulse. We show that the strong photon correlation, as induced by the atom, plays a very important role in stimulated emission. Additionally, the temporal duration of the incident photon pulse is shown to have a marked effect on stimulated emission and atomic lifetime.

Dynamics of coherent and incoherent emission from an artificial atom in a 1D space

We study dynamics of a two-level superconducting quantum system, analogous to a natural atom in an open space, by measuring the evolution of its coherent and incoherent emission. The emitted waves containing full information about the states of the artificial atom are efficiently collected due to strong atom-transmission-line coupling. This allows us to do simultaneous measurements of all the quantum state projections and perform a full characterization of the system. We derive coherence times and extract the two-time correlation function from the dynamics of the coherent emission.