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arXiv:2202.00626 · Quantum Science and Technology

Production of Fock mixtures in trapped ions for motional metrology

Antonis Delakouras, Daniel Rodríguez, Javier Cerrillo

Published Oct 10, 2023• 5 citations
arXivHTMLPDF

Abstract

Abstract We present a protocol to produce a class of non-thermal Fock state mixtures in trapped ions. This class of states features a clear metrological advantage with respect to the ground state, thus overcoming the standard quantum limit without the need for full sideband cooling and Fock-state preparation on a narrow electronic transition. The protocol consists in the cyclic repetition of red-sideband (RSB), measurement and preparation laser pulses. By means of the Kraus map representation of the protocol, it is possible to relate the length of the RSB pulses to the specific class of states that can be generated. With the help of numerical simulations, we analyse the parametric regime where these states can be reliably reproduced.

DOI
10.1088/2058-9565/ad01d7

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Abstract We present a protocol to produce a class of non-thermal Fock state mixtures in trapped ions. This class of states features a clear metrological advantage with respect to the ground state, thus overcoming the standard quantum limit without the need for full sideband cooling and Fock-state preparation on a narrow electronic transition. The protocol consists in the cyclic repetition of red-sideband (RSB), measurement and preparation laser pulses. By means of the Kraus map representation of the protocol, it is possible to relate the length of the RSB pulses to the specific class of states that can be generated. With the help of numerical simulations, we analyse the parametric regime where these states can be reliably reproduced.
We propose a fast laser pulse sequence for the generation of non-thermal Fock state mixtures of the motion of a trapped ion, targeted at displacement metrology beyond the standard quantum limit. Using a polaron-frame description of the ion-laser interaction, we identify a resonant operating point-zero detuning and a Rabi frequency matching the trap frequency-at which selective population trapping survives strong driving, enabling preparation speeds beyond the weak-driving limit of previous protocols without requiring ground-state cooling. We trace the residual infidelity at large Lamb-Dicke parameter ηηη to a single coherent process, the counter-rotating blue-sideband term neglected in the rotating-wave approximation, and show that it is suppressed by two routine calibrations: a percent-level refocusing of the pulse duration and a small compensating Bloch-Siegert detuning. Numerical simulations of the full sequence show that this refinement keeps the preparation error at or below the 10%10\%10% level up to η≈0.5η\approx0.5η≈0.5 and restores the displacement-sensing Fisher information that the uncorrected protocol loses at strong coupling, recovering up to 9 dB relative to the nominal sequence.
The quantum noise of the vacuum limits the achievable sensitivity of quantum sensors. In non-classical measurement schemes the noise can be reduced to overcome this limitation. However, schemes based on squeezed or Schrödinger cat states require alignment of the relative phase between the measured interaction and the non-classical quantum state. Here we present two measurement schemes on a trapped ion prepared in a motional Fock state for displacement and frequency metrology that are insensitive to this phase. The achieved statistical uncertainty is below the standard quantum limit set by quantum vacuum fluctuations, enabling applications in spectroscopy and mass measurements.
Quantum noise is a fundamental limitation for quantum sensors and results in the so-called shot-noise limit. Nowadays, several systems such as optical clocks or gravitational wave detectors approach measurement sensitivities where this limitation poses a major contribution to the total statistical uncertainty. It is known that this limit can be overcome by preparing the probe in a non-classical state. We will give an overview over the different non-classical states that have been implemented in the motion of single trapped ions and discuss their individual advantages and limitations in metrology. Possible applications for the presented experiments are the measurement of small oscillating electric fields and trapping frequencies. The Focus will be on our experimental work on Fock states, where quantum-enhanced sensing in both scenarios is possible with the same quantum state.
Laser-cooled trapped ions are one of the main systems used in experiments in the fields of quantum optics and quantum information. There are two commonly-used types of ion trap, the radiofrequency trap and the Penning trap. In general, the RF trap has been more widely used in quantum information experiments, meaning that the set of experimental tools for conducting these types of experiments in a Penning trap is currently less complete. The aim of the work presented in this thesis is to increase this array of tools. Our experiment uses 40Ca+ ions in a Penning trap alongside lasers. Spectroscopy has been performed on single Doppler cooled ions, and on ions that have been prepared close to their ground state of motion using a multiple-stage sideband cooling technique resulting in an average phonon occupation number of $\nzbar = 0.029\pm 0.011$ from an initial $\nzbar \approx 24$. This corresponds to a quantum ground state population of 97%97\%97%, which is close to the sideband cooling limit in our system. An axial heating rate measurement of $\dot{\bar{n}}_z=\SI{0.56\pm0.52}{\per\second}$ has also been obtained, which is the lowest recorded to date, due in part to the large dimensions of our trap. Additionally improved control of the Penning trap radial motion has been demonstrated and the average phonon occupation number of the modified cyclotron motion has been reduced from $\ncbar\approx150$ after Doppler cooling to $\ncbar=0.6$ after sideband cooling. Some preliminary single-ion coherent operations have also been performed. In the future we hope that this system of ground state cooled ions in a Penning trap can be used to generate highly-entangled states in two or more ions, with a view to performing simple quantum error-correcting codes and eventually an analogue quantum simulation of spin systems.
We have investigated theoretically and experimentally a method for preparing Dicke states in trapped atomic ions. We consider a linear chain of NNN ion qubits that is prepared in a particular Fock state of motion ∣m⟩|m⟩∣m⟩. The mmm phonons are removed by applying a laser pulse globally to the NNN qubits and converting the motional excitation to mmm flipped spins. The global nature of this pulse ensures that the mmm flipped spins are shared by all the target ions in a state that is a close approximation to the Dicke state ∣DN(m)⟩|{D}_{N}^{(m)}⟩∣DN(m)​⟩. We calculate numerically the fidelity limits of the protocol and find small deviations from the ideal state for m=1m=1m=1 and m=2m=2m=2. We have demonstrated the basic features of this protocol by preparing the Bell state ∣D2(1)⟩|{D}_{2}^{(1)}⟩∣D2(1)​⟩ in two 25Mg+{^{25}\text{M}\text{g}}^{+}25Mg+ target ions trapped simultaneously with an 27Al+{^{27}\text{A}\text{l}}^{+}27Al+ ancillary ion.
Two techniques are described that simplify the experimental requirements for measuring and manipulating quantum information stored in trapped ions. The first is a new technique using electron shelving to measure the populations of the Zeeman sublevels of the ground state, in an ion for which no cycling transition exists from any of these sublevels. The second technique is laser cooling to the vibrational ground state, without the need for a trap operating in the Lamb-Dicke limit. This requires sideband cooling in a sub-recoil regime. We present a thorough analysis of sideband cooling on one or a pair of sidebands simultaneously.