Ultra-Strong Coupling in Open Quantum Systems for Quantum Technology

A detailed exploration into quantum technology, particularly focusing on ultra-strong coupling (USC) in open quantum systems. Authored by Jishnu Rajendran<\em> and supervised by Professors Giuseppe Falci, Elisabetta Paladino, and Luigi Giannelli, the presentation covers a range of topics in the field of modern quantum technologies. It begins with an introduction, highlighting current research and potential for innovation. Then moves to various concepts of quantum technology, including quantum devices like sensors, simulators, and processors, which offer significant advantages in solving complex problems and simulating real physical systems. The presentation then examines the primary topic, interaction between light and matter, discussing models such as the Jaynes-Cummings and Quantum Rabi models, which are crucial for understanding quantum dynamics.

The discussion explores the development of quantum hardware through circuit quantum electrodynamics (circuit-QED), which allows for precise control over quantum states using superconducting circuits. These circuits enable the fabrication of transitions not found in natural atoms, enhancing the capabilities of quantum systems. The research into three-level systems and coherent trapping in small quantum networks, emphasizing their implications for quantum transport and noise resilience. Additionally, it investigates the detection of virtual photons in the USC regime, highlighting the role of entangled ground states in converting virtual photons to real ones. The presentation concludes by discussing the practical implementations of USC systems and the importance of measurement schemes in improving detection efficiency, providing a comprehensive overview of the current state and future potential of quantum technology.

Transcript

1. Ultra-Strong Coupling in Open Quantum Systems for Quantum Technology SUPERVISORS: PROF GIUSEPPE FALCI PROF ELISABETTA PALADINO PROF LUIGI GIANNELLI Jishnu Rajendran
2. OUTLINE • Introduction • Core Concepts • Research Focus • Key Findings and Contributions • Conclusion
3. Ultra-Strong Deep Strong Weak Strong Quantum system Quantum technology Technology Open Closed Classical technology Light-matter Coupling INTRODUCTION • What is it about? • Rapidly growing field • Promising innovations
4. QUANTUM TECHNOLOGY • Modern technology and its direction • What is it? Quantum Processor • General quantum simulator • Quantum computer Quantum Devices • Quantum Sensors Quantum simulators • Simulate quantum systems
5. QUANTUM TECHNOLOGY Why? • Faster at problem solving • Simulate real physical systems • Complex problems with Multi-dimensional computational space e.g. Quantum Algorithms • Shor’s Algorithm: Exponential speedup • Grover’s search algorithm: Quadratic speed-up
6. Light-Matter Interaction Two-level system interacting with a quantized field Field frequency Two-level gap Coupling
7. Light-Matter Interaction Two-level system interacting with a quantized field Cavity/resonator field qubit Qubit-field interaction
8. Jaynes–Cummings model JC Hamiltonian: RWA Conditions
9. Quantum Rabi Model Two-level Rabi Hamiltonian Counter-rotating term Rotating term • Fast counter-rotating term: can have significant contribution to the system dynamics
10. Circuit-QED • Developing quantum hardware • Control quantum states with high precision • Superconducting quantum circuits • Superconducting circuits are highly configurable. • The transitions induced by a microwave field can be engineered • Enables to fabricate transitions not seen in natural atoms.
11. Three level systems • All the configurations are possible in superconducting artificial atoms. • This can be engineered in SQC by tuning various parameter of corresponding artificial atoms.
12. Three level Λ system A three state system Single photon detuning:Δ Two-photon detuning:𝛿 The 3 level Hamiltonian in RWA The two coherent fields, pump and Stokes, induce transitions in three-levels. • Pump field couples state 0 ↔ 2, with Rabi frequency • Stokes field couples state 1 ↔ 2, with Rabi frequency
13. Stimulated Raman Adiabatic Passage (STIRAP) • An important aspect of STIRAP is the formation of the dark state. • The dark state is a coherent superposition of For mixing angle,𝜃 counterintuitive sequence
14. Coherent Trapping in Small Quantum Networks Research Focus Coherent trapping in small quantum networks T J Pope, J Rajendran, A Ridolfo, E Paladino, F M D Pellegrino and G Falci Journal of Statistical Mechanics: Theory and Experiment, Volume 2019, December 2019
15. Three level Δ system A three state system with a decay channel S The 3 level Hamiltonian • Superconducting circuits can enable us to fabricate such a network with great control over transitions
16. Δ system • We impose that dark state is one of the eigenstate of delta-system • We obtain, Darkstate eigenvalue
17. Δ system The system can be diagonalized is analogous to Autler-Townes splitting The other two eigenstate are of the form So forms a basis
18. Gaussian pulses, with pulse width T and the delay τ ≲ T Modulating the two-photon detuning for population transfer Compared to STIRAP, we have non-zero two-photon detuning We characterize the system with
19. Instantaneous eigenvalues For δp = 0, z D and z − are degenerate at some time causing efficiency to decrease due to Zener tunnelling. Delta system Lambda system Work around, δp = -2𝛺 Resulting in and preventing Zener tunnelling.
20. Delta vs Lambda STIRAP When δp = 0, the Zener tunnelling lowers the efficiency for Delta system For δp = -2𝛺 We not only recover the efficiency but also performs better P 2 magnified 30x
21. Robust • As α increases, the stable region increases. • Negative δp - more stable • Lower intermediate population • Robustness w.r.t detunings P=0.95
22. Summary: Coherent trapping in Δ systems generalizes the concept from Λ systems, with important implications for quantum transport and noise resilience. Quantum Transport: Understanding coherent trapping can aid in designing more robust quantum transport systems.
23. Virtual Photon detection in the USC Regime Research Focus Probing ultrastrong light–matter coupling in open quantum systems A. Ridolfo, J. Rajendran, L. Giannelli, E. Paladino & G. Falci Eur. Phys. J. Spec. Top. 230, 941–945 (2021).
24. Jaynes–Cummings model JC Hamiltonian: • Qubit and resonator are not too far from resonance • Total number of excitation is conserved
25. Quantum Rabi Model Total no.of excitations , is not conserved, • Cavity decay rate • Atomic decay rate Parity of N is conserved.
26. Rabi Model Ground state is an entangled state N is not conserved, but the parity is. JC model Ground state = Number of excitation is conserved Quantum Rabi Model vs JC Rabi JC Eigen-spectra for two-level system coupled to quantized field
27. Quantum Rabi Model Coupling strength Cavity decay Atomic decay Effectively characterizes the strength of coupling for different regimes Weak coupling Strong coupling Ultrastrong coupling , Deep-strong coupling } } Jaynes–Cummings model Quantum Rabi Model
28. An important and signature characteristic of USC is the existence of entangled ground state. • The presence of virtual photons in the ground state is a direct consequence of this strong interaction. • Not present in weaker coupling regimes • Can be converted to real ones with the help of an ancillary level
29. Atomic System: Three-level system with eigenstates Virtual Photon detection in the USC Regime Coupling: Ultrastrong coupling to a quantized optical mode with frequency
30. Energies of atomic level Coupled to field is uncoupled Uncoupled states and energy Entangled atom-cavity states Energies
31. At USC regime, , finite overlap of , u - g coupling can convert virtual photons in rabi space to real via ancillary space The counter-rotating terms opens a channel for the dynamical detection of virtual photons in the ground state |Φ 0 ⟩. Achieved via control pulses which probe only Rabi ground state and ancillary state, mainly by u - g transition.
32. Pump drive at frequency ω p Stokes drive at frequency ω s A two-tone pulse Almost resonant with Φ 0 −0u and Φ 0 −2u transition
33. Four level toy model We will consider a subspace spanned by Projecting the full Hamiltonian H + H C to the projection P We obtain
34. Hamiltonian in rotating frame where
35. We describe the dynamics of photodetection via Lindblad Master equation. We have two decay process, with rate
36. Cavity Dissipator Number of leaked photons Average photon current
37. We consider two-tone pulses with Gaussian envelope T - pulse width 𝜏 - pulse separation/delay
38. T - pulse width 𝜏 - pulse separation/delay t p - pulse duration t m - measurement/reset time Duration of measurement process, which in turn resets the system to ground state
39. Measurement protocol • Switchable Meter: Activated at with duration • Always-on Meter: Continuous measurement with decay rate
40. Measurement protocol: Switchable meter • Single cycle (First run): We start from the initial state |0u⟩ • Stationary map (steady-state): The dynamics is repeated after a fixed time.
41. Measurement protocol: Switchable meter • Single cycle (First run): We start from the initial state |0u⟩ • Stationary map (steady-state): The dynamics is repeated after a fixed time. Decay rate is high enough for that almost all the converted photons leave the cavity, high detection efficiency.
42. Measurement protocol: Switchable meter • Single cycle (First run): We start from the initial state |0u⟩ • Stationary map (steady-state): The dynamics is repeated after a fixed time. In case of steady-state, system is not reinitialised, resulting in less number of photons converted.
43. Measurement protocol: Switchable meter • Single cycle, First run: Larger κt m , prolonged interaction between the quantum system and the measurement.
44. Atomic spontaneous decay Atomic decay 𝛾 : These transitions are significant when an atomic spontaneous decay channel g → u exist in the full model. We neglect the decay of state e as its forbidden by selection rules.
45. For accurate simulation, we consider temperature and energy splitting Atomic dissipator with excitation rates at equilibrium Cavity decay with absorption term
46. Atomic spontaneous decay 1.99 Average photon number 1.90 T - pulse width 𝜏 - pulse separation/delay
47. : starting time of the radiative decay process This allows for the precise control over our quantum system and its operations
48. Earlier we start the cavity decay, longer the system interacts with the measurement process, which increases the average photon number Always-on meter shows better efficiency When the meter is switched-on at the later stages, detection efficiency has significantly reduced 𝜅t m =0.8
49. Always-on meter Switchable meter In this continuous measurement, the total time for the protocol is much less, making it faster Much longer, which could results in unwanted thermal effects.
50. Single-shot, First run Steady-state • Fastest protocol for small t 0 • Less measurement time • Imperfect reinitialisation
51. • Stability and robustness of Delta system in coherent trapping in small networks. • Adiabatic modulation of the system’s parameters yields coherent population transfer (analogous STIRAP). Conclusion
52. Conclusion • We analysed the dynamics of the various measurement schemes, showing that STIRAP is resilient to measurement • The detection efficiency is positively influenced by the decay rate and the duration for which the measurement apparatus is active. • Important in practical implementations of ultra-strong coupling systems.
53. Thank you
55. Backup dlides…
56. Delta system A Δ network can be implemented in superconducting architectures by working away from symmetry points but decoherence is minimized at optimal points, where one of the three couplings has to be implemented by a two-photon process At symmetry points (which means that the potential is symmetric) one needs a two-photon process to implement the third transition, and away from symmetry points one can also implement the third coupling with a one-photon transition