Quantum-optical phenomena in nanophysics

Foundations of Quantum Mechanics: Lecture 27 12.7.2013 9.2 The Casimir effect (note: chapter numbering in lecture is shifted); 9.3 Stochastic Electrodynamics   Quantum hybrid systems. Nanomechanical resonator coupled to superconducting qubit. Cantilever coupled to cold atoms. Microwave resonator coupled to NV centre spins. Nanomechanical coupling of electron spins. Single atom coupled to a vibrating membrane.

Foundations of Quantum Mechanics: Lecture 26 8.7.2013 8.3 Skyrmions; 9. Quantum electrodynamics; 9.1 Quantization of the field   4.2 Nitrogen vacancy centres in diamond. Basic structure and level scheme. Manipulation by microwaves and optical readout. Coupling to nuclear spins. Applications.

Foundations of Quantum Mechanics: Lecture 25 6.7.2013 7.2 Berry phase; 8. Particle statistics; 8.1 Fermions and bosons; 8.2 Anyons 4. Quantum optics with single solid-state emitters 4.1 Excitons in self-assembled quantum dots. Quantum dots and excitons. Single-photon source and photon correlations. Photonic crystal cavities, Purcell effect and strong coupling. Optical manipulation of spins in excitons and spin readout.

Foundations of Quantum Mechanics: Lecture 24 4.7.2013 7. Geometrical phases; 7.1 Aharonov-Bohm effect   3.9 Optomechanics outlook. Squeezed states (optical and mechanical). Entanglement light-mechanics. Test for new sources of decoherence, e.g. Penrose speculation about gravity-induced decoherence. Optomechanical crystals.

Foundations of Quantum Mechanics: Lecture 23 28.6.2013 (continued) Gravitationally-induced decoherence; 6.3 Schrödinger-Newton equation; 6.4 Other models of gravitationally induced decoherence; 6.5 Modified commutator relations   Quantum-limited displacement detection. Imprecision noise and back-action noise. The Standard Quantum Limit (SQL) for displacement detection. How it works for the case of optical detection.

Foundations of Quantum Mechanics: Lecture 22 27.6.2013 6. Extensions of Quantum Mechanics; 6.1 Spontaneous localization; 6.2 Gravitationally-induced decoherence   3.8 Quantum optomechanics. The Hamiltonian. Treating the laser drive in a rotating and displaced frame. Linearized optomechanical interaction. Quantum theory of optomechanical ground state cooling.

Foundations of Quantum Mechanics: Lecture 21 24.6.2013 5.4 Hidden-variable theories: Can they be Lorentz-invariant?; 5.5 Many-worlds; 5.6 Consistent histories   3.7 Nonlinear dynamics of optomechanical systems. Instability towards self-induced oscillations. Conditions for stable limit cycle. Power balance and force balance. Eliminating the light-field dynamics. Attractor diagram. Multistability. Possible applications.

Foundations of Quantum Mechanics: Lecture 20 20.6.2013 (continued) Nelsons Stochastic Quantization (deriving the Schrödinger equation from a condition on a drift-diffusion process, nonlocality)   3.5 Optomechanical equations of motion (classical limit). 3.6 Linearized dynamics. Effective optomechanical damping rate and effective light-induced frequency shift (optical spring effect).  

Foundations of Quantum Mechanics: Lecture 19 17.6.2013 (continued) Bohms pilot wave theory (simulations of trajectories, nonlocal influences); 5.3 Nelsons Stochastic Quantization (drift and diffusion)   T6. Fluctuation spectrum and fluctuation-dissipation theorem. Displacement spectrum. Wiener-Khinchin theorem. Fluctuation-dissipation theorem. Application to the mechanical harmonic oscillator in thermal equilibrium.

Foundations of Quantum Mechanics: Lecture 18 14.6.2013 (continued) Schroedinger cats (optomechanics, superconducting rings, measures for the size of a Schroedinger cat); 5. Interpretations of Quantum Mechanics; 5.1 Kopenhagen interpretation; 5.2 Bohm s pilot wave theory 3. Optomechanics. 3.1 Introduction. 3.2 Mechanical effects of light. 3.3 Generic model of an optomechanical system. 3.4 Elementary physics (classical).  

Foundations of Quantum Mechanics: Lecture 17 13.6.2013 (continued) Quantum dynamics of open systems (path-integral approach, Feynman-Vernon influence functional); 4.4 Experimental examples of decoherence and open quantum systems (atoms, superconducting qubits, NV, etc.); 4.5 "Schrödinger cats" (macroscopic superpositions in molecule interference, optomechanics)   2.10 Circuit QED (recent developments). Multi-qubit architectures. Multi-qubit entanglement. Microwave photons on demand. Single Photon detection. Strongly driven artificial atoms (Autler-Townes splitting, Mollow triplet). New readout methods (Josephson bifurcation amplifier). Quantum simulation (Tavis-Cummings model, Bose-Hubbard model, Josephson arrays). Hybrid systems (Rydberg atoms, polar molecules, etc.).

Foundations of Quantum Mechanics: Lecture 16 10.6.2013 (continued) noise spectrum; 4.3 Quantum dynamics of open systems (Kraus operators, Lindblad master equation, examples: two-level system relaxation and dephasing, damped harmonic oscillator)   Continued with general theory of superconducting circuits. Flux representation. Node variables. Lagrangian. Hamiltonian. Phase representation vs. charge representation. Phase qubit. Flux control of a Cooper-pair box via the Aharonov-Bohm effect.  

Foundations of Quantum Mechanics: Lecture 15 7.6.2013 (continued) Basic examples of decoherence (spin, interference, beware of polaron physics); 4.2 Noise and decoherence (noise as a stochastic process, quantum noise spectrum)   Wigner density detection via parity measurement. 2.8 Generating arbitrary field states and measuring their Wigner density. Law-Eberly protocol. Santa Barbara experiment on Wigner density detection in circuit QED. 2.9 General theory of superconducting circuits (beginning).

Foundations of Quantum Mechanics: Lecture 13 31.5.2013 (continued) Weak measurements; 3.3 Observing Trajectories (including Standard Quantum Limit of displacement detection); 3.4 Examples of measurements (position, momentum, energy, charge)   The cavity grid as a multi-qubit architecture in circuit cavity QED. Quantum error correction. Shor code for bit-flip and phase errors.

Foundations of Quantum Mechanics: Lecture 12 27.5.2013 (continued) Weak measurements (including numerical quantum jump trajectories, Quantum Zeno effect, and decoherence vs. information gain);   2.7 Quantum information processing. Quantum computation, quantum simulation, and quantum communication. Quantum bits and gates. Quantum circuits. Physical implementation in circuit QED.

Foundations of Quantum Mechanics: Lecture 11 23.5.2013 (continued) Basic features of measurement (irreversibility, Everett picture of many branches); 3.2 Weak measurements   More detailed derivation of Fermi Golden Rule rates expressed via quantum noise spectra [note: in contrast to the announcement, there is no mistake in the previous lecture"s formulas]. Numerical simulations of Bloch equations for driven two-level systems. Dissipative Rabi dynamics. Spectroscopy. Power-broadening. Multi-photon transitions. Dynamics beyond the rotating-wave approximation (Bloch-Siegert shift). 2.6 Dissipative dynamics in circuit QED.

Foundations of Quantum Mechanics: Lecture 10 17.5.2013 (continued) Entanglement; 3. The measurement process; 3.1 Basic features (Stern-Gerlach example, "quantum eraser", irreversibility, example of photon-detection in the human eye)   (continued with Lindblad equations) Application to harmonic oscillator. Pure dephasing. Bloch equations for a dissipative two-level system. T1 and T2 times. Expression of decay rates via quantum noise spectra. Some comments on the general structure of Lindblad master equations, especially for numerical solutions.

T4. Dissipation in quantum systems. Relaxation. Density matrix. Lindblad Markoff master equations. Application to relaxation in a two-level system. Application to harmonic oscillator.

Continued Jaynes-Cummings model. 2.5 Jaynes-Cummings model in circuit QED. Transmission spectroscopy and avoided crossing in the strong coupling regime. Dispersive regime for non-destructive qubit readout.

2.4 The Jaynes-Cummings model - examples. T3. The Jaynes-Cummings model: solution. Level scheme. Resonant case.

(2.3 continued) Quantizing the transmission line with periodic boundary conditions. Quantizing the transmission line resonator. Coupling to a Cooper-pair box.

(2.3 continued) Quantizing the transmission line with periodic boundary conditions. Quantizing the transmission line resonator. Coupling to a Cooper-pair box.

(2.2 continued) Energy level spectrum of the Cooper pair box, approximation as a two-level system 2.3 The microwave transmission line resonator: Cavities (optical, 3D microwave), waveguides, transmission lines, discretized circuit description of a transmission line, LC oscillator, wave equation, passage to continuum limit.

Quantum electrodynamics in superconducting circuits 2.1 Some basics about superconductivity: zero resistance, Meissner-Ochsenfeld effect, critical magnetic field, Cooper pairs, the BCS gap 2.2 The Cooper pair box: tunneling between two islands, the charging energy, the tunneling term, external control via a gate charge [erratum: near the end of the lecture, the arrow for the dipole moment of the Cooper pair box was drawn in the wrong direction. It should point from the negative to the positive charge, as always.]

Many coupled oscillators and normal modes, T2. Basics of the two-level system: Pauli matrices, Bloch vector, free precession, avoided crossing in the energy spectrum, time-dependent driving (Rabi-oscillations)

From ensembles to individual quantum systems, artificial quantum systems in nanophysics, field-matter interaction is based on oscillators (field) and two-level systems (atoms) T1. Basics of the harmonic oscillator: ladder operators, coherent states, coupling two oscillators, rotating wave approximation.