Initialization of Single Spin Dressed States using Shortcuts to Adiabaticity

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Initialization of Single Spin Dressed States using Shortcuts to Adiabaticity

J. Kölbl, A. Barfuss, M. S. Kasperczyk, L. Thiel, A. A. Clerk, H. Ribeiro, and P. Maletinsky

Phys. Rev. Lett. 122, 090502 – Published 5 March 2019

Abstract

We demonstrate the use of shortcuts to adiabaticity protocols for initialization, read-out, and coherent control of dressed states generated by closed-contour, coherent driving of a single spin. Such dressed states have recently been shown to exhibit efficient coherence protection, beyond what their two-level counterparts can offer. Our state transfer protocols yield a transfer fidelity of $\sim 99.4 (2) %$ while accelerating the transfer speed by a factor of 2.6 compared to the adiabatic approach. We show bidirectionality of the accelerated state transfer, which we employ for direct dressed state population read-out after coherent manipulation in the dressed state manifold. Our results enable direct and efficient access to coherence-protected dressed states of individual spins and thereby offer attractive avenues for applications in quantum information processing or quantum sensing.

Received 11 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.090502

Physics Subject Headings (PhySH)

Quantum control Quantum information architectures & platforms

Diamond Micromechanical devices Nitrogen vacancy centers in diamond

Confocal imaging Electron spin resonance Numerical techniques Optically detected magnetic resonance

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

J. Kölbl¹, A. Barfuss¹, M. S. Kasperczyk¹, L. Thiel¹, A. A. Clerk², H. Ribeiro³, and P. Maletinsky^1,*

¹Department of Physics, University of Basel, Basel 4056, Switzerland
²Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
³Max Planck Institute for the Science of Light, Erlangen 91058, Germany

^*patrick.maletinsky@unibas.ch

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Vol. 122, Iss. 9 — 8 March 2019

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Images

Figure 1
State transfer schematics. (a) Level scheme of the NV $S = 1$ ground state spin with spin states $| m_{s} ⟩$ (magnetic quantum number $m_{s} = 0, \pm 1$ ). All three spin transitions are individually and coherently addressable, either by MW magnetic fields ( $Ω_{1, 2} (t)$ , light and dark blue) or by a cantilever induced strain field ( $Ω$ , red), enabling a CCD. (b) Level schemes in the rotating frame for appropriate driving field phases [see text]. The initial system (left) comprises the states $| 0 ⟩$ and $| \pm ⟩$ , with the $| \pm ⟩$ being equal admixtures of $| \pm 1 ⟩$ . Ramping the amplitudes of both MW fields causes a transfer to the final dressed states $| Ψ_{k} ⟩$ ( $k = 0, \pm 1$ , right). We initialise the system in $| 0 ⟩$ , which is for adiabatic ramping transferred to $| Ψ_{+ 1} ⟩$ (orange transition). (c) Pulse sequence employed for state transfer. Note that in general $Ω_{1, 2} (t)$ have different time dependencies.
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Figure 2
Adiabatic state transfer. (a) Experimentally employed ramps for the MW field amplitudes. Both MW fields are ramped simultaneously in an optimized STIRAP pulse shape [see text]. The slope parameter $ν$ is directly linked to the ramp time $t_{r}$ . (b) Two-dimensional plots of $p_{0} = {| ⟨ 0 | ψ (t) ⟩ |}^{2}$ as a function of evolution time $t$ and ramp time $t_{r}$ . The left plot shows experimental data, and the right plot shows theoretical calculations based on a fully coherent evolution. For small $t_{r}$ oscillations in the population indicate a nonadiabatic transfer, whereas for slower ramping of the MW fields the state transfer becomes adiabatic. The green line indicates the location of the line cut presented in (c). (c) Line cut of measured population $p_{0}$ (green) as a function of evolution time $t$ for $ν = Ω / 2$ with corresponding calculation (black).
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Figure 3
STA state transfer protocol. (a) Envelope of the optimized MW field amplitudes for $ν = Ω / 2$ and $Ω / 2 π = 510 kHz$ . Modifications of the adiabatic pulse shape (dashed) lead to altered and unequal ramps for the two MW fields ( $Ω_{1}$ light blue, $Ω_{2}$ dark blue). (b) Two-dimensional plots of $p_{0}$ as a function of evolution time $t$ and ramp time $t_{r}$ . The left plot shows experimental data, and the right plot the theoretical calculations. We achieve state transfer with high fidelity independent of $t_{r}$ . The green line indicates the location of the line cut presented in (c) with ramp parameters at the experimental limit (border of grayed area). (c) Line cut of measured population $p_{0}$ (green) as function of evolution time $t$ for the same parameters as in Fig. 2 with corresponding calculation (black).
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Figure 4
Transfer fidelity and dressed state characterization. (a) Pulse sequence employed for bidirectional state transfer and manipulation of the dressed states. (b) Inverted state transfer to the initial system after the dressed state $| Ψ_{+ 1} ⟩$ was prepared. Measured population $p_{0}$ (green) as a function of the remapping time $t^{'}$ for $ν = Ω / 2$ with corresponding simulation (black). (c) Experimental transfer fidelity for various numbers of completed (re-) mapping cycles. The exponential fit to the data (dashed) yields a statistical transfer fidelity of 99.4(2) %. (d) Transition frequencies of the dressed states after initialization of $| Ψ_{+ 1} ⟩$ measured with an additional probe field $Ω_{man}$ , whose frequency is given relative to the $| 0 ⟩ \leftrightarrow | - 1 ⟩$ transition of 2.8672 GHz. (e) Rabi oscillations on a dressed state transition extracted from (d) with $Ω_{Rabi} / 2 π = 131 (1) kHz$ and $T_{dec} = 24 (3) μ s$ .
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