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arXiv:1507.06591 · Physical Review Letters

Sensing Atomic Motion from the Zero Point to Room Temperature with Ultrafast Atom Interferometry

K. G. Johnson, Brian Neyenhuis, Jonathan Mizrahi, J. David Wong-Campos, Christopher R. Monroe

Published Nov 16, 2015• 33 citations
arXivHTMLPDF

Abstract

We sense the motion of a trapped atomic ion using a sequence of state-dependent ultrafast momentum kicks. We use this atom interferometer to characterize a nearly pure quantum state with n=1 phonon and accurately measure thermal states ranging from near the zero-point energy to n[over ¯]~10^{4}, with the possibility of extending at least 100 times higher in energy. The complete energy range of this method spans from the ground state to far outside of the Lamb-Dicke regime, where atomic motion is greater than the optical wavelength. Apart from thermometry, these interferometric techniques are useful for characterizing ultrafast entangling gates between multiple trapped ions.

DOI
10.1103/physrevlett.115.213001

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Bulletin of the American Physical Society•Jan 1, 2013•1 citation
We sense the motion of a trapped atomic ion using a sequence of state-dependent ultrafast momentum kicks. We use this atom interferometer to characterize a nearly pure quantum state with n=1 phonon and accurately measure thermal states ranging from near the zero-point energy to n[over ¯]~10^{4}, with the possibility of extending at least 100 times higher in energy. The complete energy range of this method spans from the ground state to far outside of the Lamb-Dicke regime, where atomic motion is greater than the optical wavelength. Apart from thermometry, these interferometric techniques are useful for characterizing ultrafast entangling gates between multiple trapped ions.
Since the dawn of quantum information science, laser-cooled trapped atomic ions have been one of the most compelling systems for the physical realization of a quantum computer. By applying qubit state dependent forces to the ions, their collective motional modes can be used as a bus to realize entangling quantum gates. Ultrafast state-dependent kicks [1] can provide a universal set of quantum logic operations, in conjunction with ultrafast single qubit rotations [2], which uses only ultrafast laser pulses. This may present a clearer route to scaling a trapped ion processor [3]. In addition to the role that spin-dependent kicks (SDKs) play in quantum computation, their utility in fundamental quantum mechanics research is also apparent. In this thesis, we present a set of experiments which demonstrate some of the principle properties of SDKs including ion motion independence (we demonstrate single ion thermometry from the ground state to near room temperature and the largest Schrodinger cat state ever created in an oscillator), high speed operations (compared with conventional atom-laser interactions), and multi-qubit entanglement operations with speed that is not fundamentally limited by the trap oscillation frequency. We also present a method to provide higher stability in the radial mode ion oscillation frequencies of a linear radiofrequency (rf) Paul trap--a crucial factor when performing operations on the rf-sensitive modes. Finally, we present the highest atomic position sensitivity measurement of an isolated atom to date of ~0.5 nm Hz^(-1/2) with a minimum uncertainty of 1.7 nm using a 0.6 numerical aperature (NA) lens system, along with a method to correct aberrations and a direct position measurement of ion micromotion (the inherent oscillations of an ion trapped in an oscillating rf field). This development could be used to directly image atom motion in the quantum regime, along with sensing forces at the yoctonewton [10^(-24) N)] scale for gravity sensing, and 3D imaging of atoms from static to higher frequency motion. These ultrafast atomic qubit manipulation tools demonstrate inherent advantages over conventional techniques, offering a fundamentally distinct regime of control and speed not previously achievable.
We demonstrate quantum entanglement of two trapped atomic ion qubits using a sequence of ultrafast laser pulses. Unlike previous demonstrations of entanglement mediated by the Coulomb interaction, this scheme does not require confinement to the Lamb-Dicke regime and can be less sensitive to ambient noise due to its speed. To elucidate the physics of an ultrafast phase gate, we generate a high entanglement rate using just ten pulses, each of ∼20 ps duration, and demonstrate an entangled Bell state with (76±1)% fidelity. These results pave the way for entanglement operations within a large collection of qubits by exciting only local modes of motion.
We propose an adiabatic method for optimal phonon temperature estimation using trapped ions which can be operated beyond the Lamb-Dicke regime.The quantum sensing technique relies on a time-dependent red-sideband transition of phonon modes, described by the nonlinear Jaynes-Cummings model in general.A unique feature of our sensing technique is that the relevant information of the phonon thermal distributions can be transferred to the collective spin-degree of freedom.We show that each of the thermal state probabilities is adiabatically mapped onto the respective collective spin-excitation configuration and thus the temperature estimation is carried out simply by performing a spin-dependent laser fluorescence measurement at the end of the adiabatic transition.We characterize the temperature uncertainty in terms of the Fisher information and show that the state projection measurement saturates the fundamental quantum Cramér-Rao bound for a quantum oscillator at thermal equilibrium.
We report entanglement of a single atom's hyperfine spin state with its motional state in a time scale of less than 3 ns. We engineer a short train of intense laser pulses to impart a spin-dependent momentum transfer of ± 2 ħk. Using pairs of momentum kicks, we create an atomic interferometer and demonstrate collapse and revival of spin coherence as the motional wave packet is split and recombined. The revival after a pair of kicks occurs only when the second kick is delayed by an integer multiple of the harmonic trap period, a signature of entanglement and disentanglement of the spin with the motion. Such quantum control opens a new regime of ultrafast entanglement in atomic qubits.
Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of en-tangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This approach can limit the speed of entangling gates and make them vulnerable to decoherence due to coupling to unwanted modes or ion heating. This thesis is directed towards demon-strating novel entanglement schemes which are not limited by the trap frequency, and can be made almost arbitrarily fast. Towards this goal, I report here on the first experiments using ultrafast laser pulses to control the internal and external states of a single trapped ion. I begin with experiments in ultrafast spin control, showing how a single laser pulse can be used to completely control both spin degrees of freedom of the ion qubit in tens of picoseconds. I also show how a train of weak pulses can be used to drive Raman transitions based on a frequency comb. I then discuss exper-iments using pulses to rapidly entangle the spin with the motion, and how careful spectral redistribution allows a single pulse to execute a spin-dependent momentum kick. Finally, I explain how these spin-dependent momentum kicks can be used in the future to create an ultrafast entangling gate. I go over how such a gate would work, and present experimentally realizable timing sequences which would create a maximally entangled state of two ions in a time faster than the period of motion in the trap.
Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of entangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This approach can limit the speed of entangling gates and make them vulnerable to decoherence due to coupling to unwanted modes or ion heating. This thesis is directed towards demonstrating novel entanglement schemes which are not limited by the trap frequency, and can be made almost arbitrarily fast. Towards this goal, I report here on the first experiments using ultrafast laser pulses to control the internal and external states of a single trapped ion. I begin with experiments in ultrafast spin control, showing how a single laser pulse can be used to completely control both spin degrees of freedom of the ion qubit in tens of picoseconds. I also show how a train of weak pulses can be used to drive Raman transitions based on a frequency comb. I then discuss experiments using pulses to rapidly entangle the spin with the motion, and how careful spectral redistribution allows a single pulse to execute a spin-dependent momentum kick. Finally, I explain how these spin-dependent momentum kicks can be used in the future to create an ultrafast entangling gate. I go over how such a gate would work, and present experimentally realizable timing sequences which would create a maximally entangled state of two ions in a time faster than the period of motion in the trap.