Engineered quantum systems. G J Milburn Centre for Engineered - PowerPoint PPT Presentation

Engineered quantum systems. G J Milburn Centre for Engineered Quantum Systems, The University of Queensland Taipei, June 2011.

Engineered quantum systems? Superconducting qubits and microwave resonators. Entanglement via continuous measurement and feedback Nanomechanical resonators Enhanced energy transport due to vibrational modes.

Engineered quantum systems? James Clerk Maxwell, 150 years on.

Engineered quantum systems? Quantum is weird science. Wikipedia �

Engineered quantum systems? The World is Quantum AVIAN NAVIGATION EXPLOITS THE QUANTUM WORLD � The quantum chemistry of a light sensitive � molecule in the retina has a rate that depends on the � orientation with respect to the Earth ʼ s magnetic field. � For experts: single to triplet � conversion with a long lived � charge separated state. � A new model for magnetoreception , Stoneham et al 2010 �

Engineered quantum systems? The World is Quantum PHOTOSYNTHESIS EXPLOITS THE QUANTUM WORLD � Fast efficient transfer of energy through the system requires quantum effects. �

Engineered quantum systems? Quantum Principles Quantisation (energy levels) … semiconductors Tunneling … scanning tunneling microscope Uncertainty principle … quantum cryptography

Engineered quantum systems? Quantum Principles Quantisation (energy levels) … semiconductors Tunneling … scanning tunneling microscope Uncertainty principle … quantum cryptography • Superposition (coherence) Engineered • Entanglement Quantum Systems

Engineered quantum systems? The largest engineered quantum system — LIGO ... engineering the Heisenberg uncertainty principle

Engineered quantum systems?

Engineered quantum systems? -Fabricated (artificial) devices that operate by the control of quantum coherence. -Involves a very large number of atomic systems. - Quantise a collective, macroscopic degree of freedom.

Engineered quantum systems? Engineered quantum systems ... .... moving the quantum/classical border.

Superconducting qubits. Copper pair box. V G gate electrode cooper pair box cooper pair reservoir E J C g V g C J Split junction for control of E J ( φ x ).

Superconducting coplanar cavities. Si Nb Al/AlO/Al Wallraff et al., Nature (2004).

Superconducting circuit quantum electrodynamics. Superconducting qubits in a transmission line. TLA L=1cm 1 μ m for 1 GHz at T= 50 mK, _ 10 μ m n = 0.7 Girvin et al., (2003). and Blais, et al. (2004). Quality factors vary: Q = 160 at 5 . 19GHz (Schoelkopf, 2007), Q = 300 , 000 at 3 . 29GHz (Wallraff, 2009).

Circuit QED. Effective Quantisation via equivalent circuit Wallraff Nature , (2004).

The CPB Hamiltonian. ( N − n g ( t )) 2 | N �� N | − E J � � H = 4 E c | N �� N + 1 | + | N + 1 �� N | 2 N N e 2 E C = 2 C Σ C g V g ( t ) n g ( t ) = 2 e V g ( t ) = V (0) + ˆ v ( t ) g

The Hamiltonian

The Hamiltonian

The Hamiltonian Work in subspace, N = 0 , 1. n g ( t )(1 − 2 n (0) H = H CPB − 4 E C δ ˆ − ¯ σ z ) g σ z − E J H CPB = − 2 E C (1 − 2 n (0) g )¯ 2 ¯ σ x σ z = | 0 �� 0 | − | 1 �� 1 | , ¯ ¯ σ x = | 1 �� 0 | + | 0 �� 1 | n g ( t ) ≈ C g δ ˆ 2 e ˆ v ( t ) write v ( t ) = V 0 rms ( a + a † ) ˆ

The Hamiltonian H = � ω c a † a + � ǫ σ z − � ∆ σ x − � g ( a + a † )¯ 2 ¯ 2 ¯ σ z � ω c a † a : cavity field − 2 E C (1 − 2 n (0) � � ǫ = g ) controlled independently E J cos( φ e ) � ∆ = 2 � E J � 1 / 4 � g ≈ β V 0 rms 4 E C

Circuit QED Rotating wave approximation: Jaynes-Cummings . Diagonalise H CPB H = � ω c a † a + � Ω 2 σ z − � g ( a σ + + a † σ − ) � ∆ 2 + ǫ 2 Ω = Vacuum Rabi splitting

Vacuum Rabi splitting. Ω = ω c : ( | 1 , g � | 0 , e � ) degenerate e 2g g Probe the transmission of a weak coherent signal as the qubit is detuned.

Vacuum Rabi splitting Walraff group: Fink et al., Nature 454, 315 (2008) . Coupling strength: g / 2 π ∼ 154MHz.

Measurement in circuit QED. No efficient microwave photon counters exist, E µ ∼ 10 − 5 E vis

Measurement in circuit QED. No efficient microwave photon counters exist, E µ ∼ 10 − 5 E vis Directly measure voltages: Use electronic mixers (not beam splitters) for heterodyne/homodyne detection.

Measurement in circuit QED. cout bin Re[S (t)] b a Im[S (t)] b IQ mixer IQ mixer cin bout b out = √ κ b a − b in c out = √ κ c a − c in Stochastic current is conditioned on the quantum sate of the cavity field S b ( t ) = g b � a � c + η ( t ) where η ( t ) is a noise term.

Measurement in circuit QED. Example: Measurements of the Correlation Function of a Microwave Frequency Single Photon Source , Bozyigit et al. arXiv:1004.3987 Note, measurements are made on both ends of the cavity. Prepare (via qubit coherent control) a single photon state cos θ r | 0 � + sin θ r | 1 � in the cavity. S b ( t ) ∝ � a ( t ) � = sin θ r

Measurement in circuit QED.

Transmon nonlinear microwave optics. Switching a single microwave photon. Delsing group: Hoi et al., arXiv:1103.1782v1 Pump-off: probe is reflected. Pump-on: probe is transmitted. Switch a single-photon signal from an input port to either of two output ports with an on-off ratio of 90%

Transmon as a single photon detector. Bixuan Fan, Tom Stace, GJM and Goran Johansson (Chalmers): Can we detect a single photon control by a phase shift on the probe? Prepare a single photon in the source cavity at t = 0, and look at time resolved homodyne signal.

Transmon as a single photon detector. Bixuan Fan, Tom Stace, GJM and Goran Johansson (Chalmers):

Transmon as a single photon detector. Bixuan Fan, Tom Stace, GJM and Goran Johansson (Chalmers):

Quantum feedback. classical signal processing classical signal quantum continuous measurement system noise/decoherence noise/decoherence see H M Wiseman and GJM, Quantum measurement and control , CUP, 2010

Feedback control, with measurement. Feedback cooling of an optomechanical resonator. but not quantum noise limited...

Entangling two SC qubits by feedback. Usually create entangled state of two qubits via unitary control: | 0 �| 0 � → | 0 �| 1 � + | 1 �| 0 � Enable: ◮ violation of Bell inequality ◮ quantum teleportation ◮ quantum cryptography ◮ quantum computing In superconducting circuits: Matthias Steffen, et al. Science 313 , 1423 (2006);

Entangling two SC qubits by feedback. a (t) a (t) out in IQ mixer Dispersive limit: δ = ω c − ω q ≫ g ∼ 10MHz Effective Hamiltonian in the interaction picture. H I = χ a † a ( | 1 �� 1 | − | 0 �� 0 | ) ≡ χ a † a σ z Conditional frequency shift of cavity.

Entangling two SC qubits by feedback. Sarovar, Goan, Spiller , GJM, Phys. Rev. A, 72, 062327 (2005)* Two CPB qubits, dispersive limit. H I = 2 χ J z a † a + χ ( σ + 1 σ − 2 + σ − 2 σ + 1 ) where J z = σ z 1 + σ z 2 . e − i θ J z a † a ( | 00 > + | 01 > + | 10 > + | 11 > ) | α � | 00 �| α e i θ � + | 11 �| α e − i θ � + ( | 10 � + | 01 � ) | α � = Measure phase of field by homodyne detection. * See also ”Tunable joint measurements in the dispersive regime of cavity QED”, Lalumi` ere, Gambetta, Blais arXiv:0911.5322

Entangling two SC qubits by feedback. Y |00> X |01>+|10> |11> Nemoto & Munro. PRL 2004.

Continuous conditional evolution. V(t) i(t): classical signal out driving t local oscillator The homodyne current for quantum limited detection obeys dI ( t ) = κ � a + a † � + √ κ dW ( t ) Assume the only source of noise in the signal comes from the quantum source. What is the conditional state of the source, conditioned on a particular current history, i ( t ).

Feedback creation of entanglement. signa processing feedback to qubit bias V(t) driving local oscillator Feedback homodyne current from SET to change bias conditions of the CPB. Process signal by low-pass filter: � t R ( t ) = 1 e − γ ( t − t ′ ) dI ( t ′ ) N t − T Add control Hamiltonian H FB = λ R ( t ) 3 ( σ x 1 + σ x 2 )

Feedback creation of entanglement. d | ψ c ( t ) � = [ − iH I − iH FB ( t ) − κ a † a ] | ψ c ( t ) � dt + dI ( t ) a | ψ c ( t ) � evolution of entanglement average over 300 trajectories.

Feedback creation of entanglement. fidelity for |01>+|10> 99% of trajectories converge to target state. Sarovar et al., Phys. Rev. A 72, 062327 (2005)

Fabrication of nanomechanical systems. mask e t a r t s b u s sacrifical layer mask Roukes, Physics World, Feb, 2001. Roukes, Physics World, 2001.

Quantum nanomechnical systems. � ν > k B T Fundamental resonance frequency of a mechanical bar: M.L. Roukes, "Nanoelectromechanical Systems", cond-mat/0008187 Roukes, 2000.

SC qubits + nanomechanics. Nanomechanical measurements of a superconducting qubit LaHaye, Suh, Echternach, Schwab & Roukes, Nature, (2009)

SC qubits + nanomechanics. Nanomechanical resonator is driven capacitively Qubit is driven by microwaves, Measure resonator frequency shift as charge ( ǫ ) and tunneling (∆) bias of qubit are changed.