Quantum control of 88Sr+ in a miniature linear Paul trap

Akerman, Nitzan; Glickman, Yinnon; Kotler, Shlomi; Keselman, Anna; Ozeri, Roee

doi:10.1007/s00340-011-4807-6

Appl. Phys. B

2011

DOI: 10.1007/s00340-011-4807-6

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Quantum control of 88Sr+ in a miniature linear Paul trap

Nitzan Akerman

Yinnon Glickman

Shlomi Kotler

et al.

Abstract: We report on the construction and characterization of an apparatus for quantum information experiments using 88 Sr + ions. A miniature linear radio-frequency (rf) Paul trap was designed and built. Trap frequencies above 1 MHz in all directions are obtained with 50 V on the trap end-caps and less than 1 W of rf power. We encode a quantum bit (qubit) in the two spin states of the S 1/2 electronic ground-state of the ion. We constructed all the necessary laser sources for laser cooling and full coherent manipulat… Show more

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Cited by 26 publications

(19 citation statements)

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“…Essentially, our apparatus enabled us to place the electronic spins at a controlled distance from one another, as well as initialize, manipulate and detect their internal spin state with high fidelity. Details of the setup are found in Ref 27 as well as in the Supplementary Information.…”

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confidence: 99%

Measurement of the magnetic interaction between two bound electrons of two separate ions

Kotler

Akerman

Navon

et al. 2014

Nature

141

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Electrons have an intrinsic, indivisible, magnetic dipole aligned with their internal angular momentum (spin)1 . The magnetic interaction between two electrons can therefore impose a change in their spin orientation. Similar dipolar magnetic interactions exists between other spin systems and were studied experimentally. Examples include the interaction between an electron and its nucleus or between several multi-electron spin complexes 2-8 . The process for two electrons, however, was never observed in experiment. The challenge is two-fold.At the atomic scale, where the coupling is relatively large, the magnetic interaction is often overshadowed by the much larger coulomb exchange counterpart 2 . In typical situations where exchange is negligible, magnetic interactions are also very weak and well below ambient magnetic noise. Here we report on the first measurement of the magnetic interaction between two electronic spins. To this end, we used the ground state valence electrons of two 88 Sr + ions, co-trapped in an electric Paul trap and separated by more than two micrometers.We measured the weak, millihertz scale (alternatively 10 −18 eV or 10 −14 K), magnetic interaction between their electronic spins. This, in the presence of magnetic noise that was six * Current address: Physical Measurement

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mentioning

confidence: 99%

Measurement of the magnetic interaction between two bound electrons of two separate ions

Kotler

Akerman

Navon

et al. 2014

Nature

141

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“…In general these rotations require single-qubit addressing capability. For our purpose, a single discriminatory transition is sufficient for all the required operations.In our setup, we use 88 Sr + ions confined in a linear Paul trap [19]. We work with optical qubits that are encoded in the |S = 5S 1/2,+1/2 ground state level and in the |D = 4D 5/2,+3/2 meta-stable level which has a 1/e lifetime of 390 ms [20].…”

mentioning

confidence: 99%

“…In our setup, we use 88 Sr + ions confined in a linear Paul trap [19]. We work with optical qubits that are encoded in the |S = 5S 1/2,+1/2 ground state level and in the |D = 4D 5/2,+3/2 meta-stable level which has a 1/e lifetime of 390 ms [20].…”

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confidence: 99%

Quantum process tomography of a Mølmer-Sørensen interaction

et al. 2014

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We report the quantum process tomography of a Mølmer-Sørensen entangling gate. The tomographic protocol relies on a single discriminatory transition, exploiting excess micromotion in the trap to realize all operations required to prepare all input states and analyze all output states. Using a master-slave diode lasers setup, we demonstrate a two-qubit entangling gate, with a fidelity of Bell state production of 0.985(10). We characterize its χ-process matrix, the simplest for an entanglement gate on a separable-states basis, and we observe that the dominant source of error is accurately modelled by a quantum depolarization channel. PACS numbers:The ability to realize and characterize high-fidelity two-qubit gates is central for quantum information science as, together with single-qubit rotations, they constitute the building blocks for quantum computation [1]. The detailed characterization of these gates is therefore crucial. Quantum Process Tomography (QPT) is an important method to fully characterize linear quantum processes. In particular, QPT of two-qubit entangling gates has been used to characterize CNOT gates in linear-optic [2], NMR [3], as well as trapped ions [4,5], or a square root i-SWAP gate with superconducting qubits [6]. In trapped-ions experiments, Mølmer-Sørensen (MS) entangling gates [7] have become increasingly popular, both for quantum computation purposes [8,9] and for inducing effective spin-spin couplings that allow to simulate complex quantum many-body hamiltonians from condensed matter physics [10]. One of its main advantages as compared with other gate protocols is its first-order insensitivity to the phonon occupation number (i.e. temperature of the ion-crystal), which allowed, inter alia, the highest entangled state production fidelity reached to date (0.993(1) [11]), entanglement between ions in thermal motion [12], as well as the creation of a maximally entangled state of a large (N = 14) number of qubits [13]. In this letter, we first implement a new and simple protocol for QPT with trapped ions, which only requires a single discriminatory transition. The scheme is based on inhomogeneous micromotion in the trap that enables addressing single qubits in the chain [14][15][16]. Subsequently, we realize the tomographic reconstruction of a Mølmer-Sørensen interaction which, despite its growing importance, has not been process-analyzed yet.A quantum process is defined as a completely positive map E in the space of density matrices. Given a complete set of operators {A i } (such that j A † j A j = I), the * These authors contributed equally to this work. † Present email and address: nn270@cam.ac.uk, Cavendish Laboratory, University of Cambridge, J.J. Thomson Ave., Cambridge CB3 0HE, United Kingdom output state for an arbitrary input state ρ can be written as (for details see for instance [3,17,18])(1)Here {χ ab } is the process matrix (with 4 n × 4 n elements for n qubits), which contains the full information on the process E and is measured by QPT. A convenient set of input states for t...

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“…We experimentally implement the fast dynamically decoupled gate with trapped ions and demonstrate its robustness to noise. Two 88 Sr+ ions are spatially confined in a linear Paul trap with an axial frequency of ν = 1.67 MHz and radial frequencies of ∼ 4 MHz [37]. A qubit is encoded on Zeeman-splitted sublevels of the 5S 1/2 (m = −1/2) → 4D 5/2 (m = 1/2) optical electricquadrupole transition of each ion with a natural lifetime of ∼ 0.4 seconds.…”

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confidence: 99%

Fast Dynamical Decoupling of the Mølmer-Sørensen Entangling Gate

et al. 2017

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Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of √ N , with N being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of π 2 , independently of the number of pulses applied. We experimentally demonstrate the robustness of our fast dynamically decoupled entangling gate to σz noise with ions in a Paul trap.High quality on-demand generation of entanglement is a necessary condition for quantum information processing and quantum metrology. While for some physical platforms entanglement is generated by an inherent direct interaction between subsystems, various platforms of interest make use of a mediating boson with spindependent coupling. For instance, the interaction between trapped ions is carried via a vibrational phonon [1][2][3][4][5][6][7][8][9][11][12][13]; superconducting qubits are entangled via a microwave photon [16][17][18]; the interaction between distant NVs can be carried via a nanomechanical oscillator's phonon [19,20] and a cavity photon carries the interaction between atoms in cavity QED architectures [21,23,24]. The common Hamiltonian representing these quantum systems is of the formwith σ α,i representing the Pauli matrix in the α direction of the i th spin. In the trapped ion case this Hamiltonian allows one to execute the Mølmer-Sørensen (MS) gate [1]. After times 2πn/ε for an integer n, the boson is disentangled from the spins, leaving the spins entangled via a geometric phase which is proportional to the area of the closed circle traced by the boson trajectory in phase space [2, 3,25].Despite considerable progress in achieving high-fidelity entanglement in recent years, entanglement fidelity remains a primary obstacle for performance of large scale quantum information processing, and more particularly fault-tolerant quantum computation. Attempts to improve the fidelity of entangling gates must overcome the limitations imposed by environmental noise as well as imperfections in the control apparatus. Dynamical decoupling is a common method for fighting the effects of noise. When utilizing dynamical decoupling pulses [26,27] during the entangling gate operation, one is required to consider the affect on the spin dependent coupling to the mediating boson. In many experiments, a sing...

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Quantum control of 88Sr+ in a miniature linear Paul trap

Cited by 26 publications

References 36 publications

Measurement of the magnetic interaction between two bound electrons of two separate ions

Measurement of the magnetic interaction between two bound electrons of two separate ions

Quantum process tomography of a Mølmer-Sørensen interaction

Fast Dynamical Decoupling of the Mølmer-Sørensen Entangling Gate

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