We have been in the same subgroup for the entire period of my PhD and this human-to-human interaction has been the direct cornerstone of my thesis work. In the group, students and postdocs come and go, but the "fabulous ones" are always there.
INTRODUCTION
- Quantum information science
- Superconducting circuits
- Quantum light-matter interfaces
- Outline of the thesis
For quantum devices with more than 50 individually controllable qubits (see, e.g., the fidelity of arbitrary single-qubit control is above 99.9%, the two-qubit entanglement gate fidelity is above 99.5%, and the fidelity of single-shot individual qubit readout output is above 95%. In the other limit, when the quantized light fields are in their ground state (i.e. the vacuum), the process of the atom starts from a higher-energy (excited) state and radiates into its surrounding light fields can be described by spontaneous emission (Fig.1.4a).
WAVEGUIDE QUANTUM ELECTRODYNAMICS
Waveguide QED with linear dispersion
Intuitively, this can be explained by the interference of the emission of the two emitters: the relative phase in the bright (dark) state causes the light field of the two emitters to interfere constructively (destructively) so that the emission is twice as strong (completely suppressed ), see Fig.2.3a (b). This cavity-mediated exchange interaction can be seen as the presence of one emitter modifying the Lamb shift of the other, i.e. the emission of a virtual photon from one emitter to the cavity mode which is absorbed by the other emitter.
Waveguide QED in the bandgap regime
The properties of the bound state are determined by the resonance between the bound state and the band. This tuning of the bound state properties serves as the basis for the tunable exchange interaction discussed in the following subsection.
ENGINEERING AND OPERATING A SUPERCONDUCTING WAVEGUIDE QED SYSTEM
Circuit design
For example, the fundamental mode of standing wave resonances, formed by open/short circuit boundary conditions, is used as a readout mode. Another design for the resonator is the inductance-capacitance (LC) resonator design with joined elements, for example those used in [170].
Device fabrication and packaging Device fabricationDevice fabrication
Any error in e.g. the thin wire coil (Fig. 3.4a), will change the resonant frequency of the waveguide resonator, which will create defect modes or even disrupt the band structure. The interconnection of the SMPM connectors (Fig.3.5a) deteriorates after thermal cycling, causing the electrical connection to a few connectors to fail under cryogenic temperature.
Experimental setup and operation
The Bluefors LD-250 DF we use is designed to be electrically floating (>1MΩ), isolated from the gas handling unit and DF frame, so that it can be connected to a clean ground. From the above analysis, we see that the cryostat ground is still inevitably connected to the ground ground at numerous points, forming ground loops (Fig. 3.6a).
CAVITY QUANTUM ELECTRODYNAMICS WITH ATOM-LIKE MIRRORS
- Introduction
- Theoretical formalism
- Experimental results
- Conclusion and outlook
- Methods FabricationFabrication
D⟩ is coupled to the excited state of the probe qubit|e⟩pat with a cooperatively enhanced rate of 2J =p. In Figure 4.4, we show the timing diagram and plot three measured curves of the population dynamics of the probe qubit with respect to τ. Finally, we measure the state of the probe qubit and perform an exponential fit of the resulting decay curve.
QUANTUM ELECTRODYNAMICS IN A TOPOLOGICAL WAVEGUIDE
- Introduction
- Description of the topological waveguide
- Properties of quantum emitters coupled to the topological waveguide The non-trivial properties of the topological waveguide can be accessed by couplingThe non-trivial properties of the topological waveguide can be accessed by coupling
- Quantum state transfer via topological edge states
- Discussion and outlook
In general, bound states with a symmetric photonic envelope arise due to the inversion symmetry of the photonic bath with respect to the qubit location [120]. Mimicking the topological edge state, the induced photonic envelope of the bound state faces right (left) with photon occupation only at B (A) sites (Fig. 5.3b), while. The opposite directionality is expected in the case of the topological phase of the waveguide.
A SUPERCONDUCTING QUANTUM SIMULATOR BASED ON A PHOTONIC-BANDGAP METAMATERIAL
- Introduction
- Metamaterial-based quantum simulator
- Bose-Hubbard model with long-range hopping
- Many-body Hamiltonian learning
- Ergodic many-body dynamics with long-range hopping
- Conclusion and outlook
Specifically, we observe the probability distribution of a bitwise set of results that reflects the ergodic nature of the Hamiltonian with long-range jumps. Ouch decreases as ω01 approaches the nearest band edge due to dressing from the band modes of the metamaterial [163], i.e. Lamb's shift. Another decoherence probe is a histogram P(pz) of the measured bit string probabilities (Figure 6.6b, right).
FUTURE DIRECTIONS
The extended version of the Bose-Hubbard model: ground state proper- tiesties
We specify the initial state particle number that is retained throughout the simulation, which effectively takes care of the chemical potential. More specifically, the boundary of the phase diagram corresponds to the chemical potential µp(m) or the energy required to add (subtract) one particle, which can be obtained from the ground state energy difference between the particle number N = LandL+ 1(L−1 ) in the system where this is the system size. Using this method we obtain the critical value as a function of ξ in the two band gaps3 (Fig.7.2c).
Engineering the coupling profile
ˆb†i + ˆbi) (7.2) can be added to the Hamiltonian so that in the rotating frame of the driving frequency the separation between the driving and the qubit is controlled by the chemical potentialµ. This method is based on the incompressibility of e.g. of the MI phase and achieves a balance between propulsion and dissipation to stabilize the number of particles to a uniform charge. The sideband strength, controlled by the modulation frequency and power, determines the strength of the corresponding exponential profile in combination.
Scaling up to a large system size
The quantum bus is shared between all qubits to mediate long-range interactions, while multiple metamaterial Purcell filters are incorporated, each of which can host around 10 readout resonators. Cartoon showing a real scaled wave QED architecture where the middle blue structure represents the wave bus to mediate the qubit-qubit interaction, the orange rectangles represent the qubits, the colors of the readout resonators represent different frequencies, and the green structures are the readout - From the supply lines cutting 10 readout resonators into a single supply line. The important factor is the gate speed in the long-range limit, where the passband modes approach continuity in frequency and the gate is mediated by a collection of passband modes.
BIBLIOGRAPHY
49] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Josɛf C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fɛdinand G. S. L. Brandao, Devid A Buell, ɛn ɔda pipul dɛn. 77] Rami Barends, Lamata L, Julian Kɛli, Garsia-Alvarez L, Ɔstin G Fawla, Mɛgrant A, Ivan Jɛfri, Tɛd C Wait, Daniɛl Sank, Jɔsh Y Mutus, ɛn ɔda pipul dɛn. 169] Rami Barends, Julian Kɛli, Antɔni Mɛgrant, Daniɛl Sank, Ivan Jɛfri, Yu Chɛn, Yi Yin, Bɛn Chiaro, Jɔsh Mutus, Chals Nil, ɛn ɔda pipul dɛn.
DEVICE FABRICATION DETAILS
SUPPLEMENTARY INFORMATION FOR CHAPTER 4
- Spectroscopic measurement of individual qubits
- Detailed modeling of the atomic cavity
- Lifetime (T 1 ) and coherence time (T 2 ∗ ) of dark state
- Shelving
The dark state decay rate scales as Γ1D,D ≈Γ1D(∆ϕ)2/2, which makes only a small contribution to the dark state decay rate. 2Ω1, whereΩ1 is the Rabi frequency of one of the mirror qubits of the probe signal along the waveguide. In the measurement, we use the state transfer protocol to transfer part of the ground state population to the dark state.
SUPPLEMENTARY INFORMATION FOR CHAPTER 5
Modeling of the topological waveguide
We first consider the band structure of the system within the rotating wave approximation (RWA), discarding the counter-rotating terms ˆaˆb and ˆa†ˆb† i. The Zak phase of photonic bands is determined by the behavior of f(k) in the complex plane . The knowledge of the transformation Sk allows us to evaluate the Zak phase of photonic bands.
Mapping of the system to the SSH model and discussion on robustness of edge modesedge modes
Chiral symmetry is preserved in the presence of coupling disorders between different types of sub-lattice along the chain, ensuring stability in the frequency of the edge modes. To study the stability of the edge mode frequencies in our circuit model, we perform a simulation on different types of perturbation realizations in the circuit illustrated in Fig.C.1. C.4b we observe strong fluctuations in the frequencies of the edge modes even at a slight disorder level of r = 0.1.
Device I characterization and Experimental setup
An interesting observation in Fig. C.4b is the stability of the frequencies of the modes in the upper passband with respect to the disturbance in Cv and Cw. The meaning of each symbol in the diagram on the left is listed on the right. The tapered part is colored in the same way as the corresponding components in the panels.
Tapering sections on Device I
Both output lines are amplified by a single High Electron Mobility Transistor (HEMT) on board 4K followed by room temperature amplifiers at 300 K. S11 can be measured by sending an input signal to Waveguide Input 1 and collecting the output signal from Waveguide Output 2 with both 2×2 switches in a cross (×) configuration. We find a good agreement in the frequency of the normal modes and the ripple rate between the theoretical model and the experiment, as shown in Fig. C.7c.
Directional shape of qubit-photon bound state
When the qubit frequency resonates with the reference frequencyω0, the subsystem S2 can be viewed as a semi-infinite array in the topological phase, with the qubit effectively acting as an edge location. Here the subsystem S′1 (S′2) is a semi-infinite array in the topological phase extending to the left (right), where the last location hosting the topological edge mode E′1(E′2) is atω=ω0 the A (B) sublattice of the then unit cell. Here g˜ (J˜v) is the coupling between edge mode E′1 and the qubit (edge mode E′2), diluted from g (Jv) due to the mixing of photonic occupancy at locations other than the boundary in the region. edge modes.
Coupling of qubit-photon bound states to external ports at different fre- quenciesquencies
The condition notation with prime (double prime) in subpanel i. iii.) indicates the imperfect superradiant bright state and the subradiant dark state, where the width of orange arrows specifies the strength of the coupling of states to the waveguide channel. Within the upper bandgap (7.485 GHz), the coupling of qubit photon-bound states to external gates decreases monotonically with the distance from the qubit site to the gate, regardless of which sublattice the qubit is coupled to (Fig. C.9b) . Note that we find that the external coupling to port 2 (κe,2) is generally smaller than that to port 1 (κe,1), which may result from a small impedance mismatch when connecting the device to the external wiring.
Probing band topology with qubits Signature of perfect super-radianceSignature of perfect super-radiance
This behavior is similar to that of qubit-photon bound states formed in a uniformly coupled structure, where the bound states exhibit a symmetric photonic envelope surrounding the qubit. Here, the two-qubit transfer matrix accounts for pure dephasing, which causes the sharp peaks in sub-panels (i.) and (iii.) of Fig.C.10b to lie below the perfect transmission level (unity ) as contrary to the prediction from the ideal case of electromagnetically induced transparency [222].
