Generating quantum entanglement in large systems on time scales much shorter than the coherence time is key to powerful quantum simulation and computation. Trapped ions are among the most accurately controlled and best isolated quantum systems [1] with low-error entanglement gates operated via the vibrational motion of a few-ion crystal within tens of microseconds [2]. To exceed the level of complexity tractable by classical computers the main challenge is to realise fast entanglement operations in large ion crystals [3,4]. The strong dipole-dipole interactions in polar molecule [5] and Rydberg atom [6,7] systems allow much faster entangling gates, yet stable state-independent confinement comparable with trapped ions needs to be demonstrated in these systems [8]. Here, we combine the benefits of these approaches: we report a 700 ns two-ion entangling gate which utilises the strong dipolar interaction between trapped Rydberg ions and produce a Bell state with 78% fidelity. The sources of gate error are identified and a total error below 0.2% is predicted for experimentally-achievable parameters. Furthermore, we predict that residual coupling to motional modes contributes ∼ 10 −4 gate error in a large ion crystal of 100 ions. This provides a new avenue to significantly speed up and scale up trapped ion quantum computers and simulators. Trapped atomic ions are one of the most promising architectures for realizing a universal quantum computer [1]. The fundamental single-and two-qubit quantum gates have been demonstrated with errors less than 0.1% [2], sufficiently low for fault-tolerant quantum errorcorrection schemes [10]. Nevertheless, a scalable quantum computer requires a large number of qubits and a large number of gate operations to be conducted within the coherence time.Most established gate schemes using a common motional mode are slow (typical gate times are between 40 and 100 µs) and difficult to scale up since the motional spectrum becomes more dense with increasing ion number. Many new schemes have been proposed [11][12][13][14], with the fastest experimentally-achieved gate being 1.6 µs (99.8% fidelity) and 480 ns (60% fidelity) [15], realised by driving multiple motional modes simultaneously. Although the gate speed is not limited by the trap frequencies, the gate protocol requires the phase-space trajectories of all modes to close simultaneously at the end of the pulse sequence [15]. In long ion strings with a large number of vibrational modes, it becomes increasingly challenging to find and implement laser pulse parameters that execute this gate with a low error. Thus, a slow-down of gate speed appears inevitable.Two-qubit entangling gates in Rydberg atom systems are substantially faster, owing to strong dipole-dipole interactions. The gate fidelities in recent experiments using neutral atoms are fairly high [16,17]. However, the atom traps need to be turned off during Rydberg excitation. This can cause unwanted coupling between qubits and atom motion as well as atom loss [8,18]. Employing blue-detune...

Trapped Rydberg ions are a promising novel approach to quantum computing and simulations [1][2][3]. They are envisaged to combine the exquisite control of trapped ion qubits [4] with the fast two-qubit Rydberg gates already demonstrated in neutral atom experiments [5][6][7]. Coherent Rydberg excitation is a key requirement for these gates. Here, we carry out the first coherent Rydberg excitation of an ion and perform a single-qubit Rydberg gate, thus demonstrating basic elements of a trapped Rydberg ion quantum computer.Systems of trapped ion qubits have set numerous benchmarks for single-qubit preparation, manipulation, and readout [8]. They can perform low error entanglement operations [9,10] with up to 14 ion qubits [11]. Still, a major limitation towards realizing a large-scale trapped ion quantum computer or simulator is the scalability of entangling quantum logic gates [12].Arrays of neutral atoms in dipole traps offer another promising approach to quantum computation and simulation. Here, qubits are stored in electronically low-lying states and multi-qubit gates may be realized by exciting atoms to Rydberg states [6,7,13,14]. Rydberg states are exotic states of matter in which the valence electron is excited to high principal quantum numbers. They can have extremely high dipole moments and may interact strongly with each other, which has allowed entanglement generation [15,16] and fast two-qubit Rydberg gates [5] in neutral atom systems.A system of trapped Rydberg ions may combine the advantages of both technologies. Electronically lowlying states may be used as qubit states and fast multiqubit gates are envisaged by coherently exciting ions to Rydberg states and employing dipolar interactions between them [1,17]. Multi-qubit gates commonly used in trapped ion systems suffer scalability restrictions due to spectral crowding of motional modes [12]. This issue does not affect multi-qubit Rydberg gates thus a trapped Rydberg ion quantum computer offers an alternate approach to a scalable system. An unanswered question was whether trapped ions can be excited to Rydberg states in a coherent fashion as is required for multi-qubit Rydberg gates. In our experiment we study a single 88 Sr + ion confined in a linear Paul trap. Three atomic levels in a ladder configuration are coupled using two UV lasers (Fig. 1). The qubit state |0 is coupled to the excited state |e by the pump laser at 243 nm with Rabi frequency Ω P . |e is coupled in turn to the Rydberg state |r (42S 1/2 , m J = −1/2) using the Stokes laser at 307 nm with Rabi frequency Ω S . The experimental setup is described in detail in the Methods section and in [3].We can use the two-photon coupling for coherent control of the Rydberg excitation. At two-photon resonance (|0 to |r ) the coupling Hamiltonian has a "dark" eigenstate |Φ dark ∼ Ω S e iφ |0 − Ω P |r (Methods), which is named so because it does not contain any component of |0-|rRydberg excitation by STIRAP shown by comparing application of the single and the double STIRAP pulse sequences. The sin...

Trapped Rydberg ions are a promising new system for quantum information processing. They have the potential to join the precise quantum operations of trapped ions and the strong, longrange interactions between Rydberg atoms. Technically, the ion trap will need to stay active while exciting the ions into the Rydberg state, else the strong Coulomb repulsion will quickly push the ions apart. Thus, a thorough understanding of the trap effects on Rydberg ions is essential for future applications. Here we report the observation of two fundamental trap effects. First, we investigate the interaction of the Rydberg electron with the quadrupolar electric trapping field. This effect leads to Floquet sidebands in the spectroscopy of Rydberg D-states whereas Rydberg S-states are unaffected due to their symmetry. Second, we report on the modified trapping potential in the Rydberg state compared to the ground state which results from the strong polarizability of the Rydberg ion. We observe the resultant energy shifts as a line broadening which can be suppressed by cooling the ion to the motional ground state in the directions orthogonal to the excitation laser.PACS numbers: 32.80. Ee, 37.10.Ty, 32.60.+i Trapped ions are one of the most mature implementations of a quantum computer. The trapped ion approach has set several benchmarks with qubit lifetimes up to minutes [1], entanglement operations with error probabilities smaller than 10 −3 [2, 3], and with up to 14 entangled qubits [4]. Trapped ions also assume a leading role in the implementation of quantum algorithms [5][6][7][8], quantum error correction [9][10][11], and quantum simulations [12][13][14][15].The standard method to realize quantum information processing with trapped ions employs the common motion for entanglement operations between the ion qubits [16]. A current limitation of trapped ion quantum computation is the limited storage capacity as it becomes more difficult to perform entanglement operations in large ion crystals due to the increasingly complex motional mode structure. Possible schemes to reach larger quantum systems include segmented ion traps [17], ionphoton networks [18], and, trapped Rydberg ions [19,20].Trapped Rydberg ions are a novel quantum system. Here, the outermost electron of an ion is excited into Rydberg states far away from the atomic core. Due to large generated dipole moments, Rydberg ions are envisioned to sense each other by means of a dipolar interaction. The advantage of the Rydberg interaction is that it does not depend on the motional mode structure, thus it may be used in larger ion crystals for entanglement operations [19,21,22]. A similar entanglement method has been demonstrated with neutral atoms [23][24][25]. In this sense trapped Rydberg ions promise to join the advantages of both technologies: they combine the strong dipolar interaction between Rydberg atoms with the precise quantum control and long storage times of trapped ions.Recently, trapped Rydberg ions have been realized for the first time using a single-photon ...

Usually the influence of the quadratic Stark effect on an ion's trapping potential is minuscule and only needs to be considered in atomic clock experiments. In this work we excite a trapped ion to a Rydberg state with polarizability ∼ eight orders of magnitude higher than a low-lying electronic state; we find that the highly-polarizable ion experiences a vastly different trapping potential owing to the Stark effect. We observe changes in trap stiffness, equilibrium position and minimum potential, which can be tuned using the trapping electric fields. These effects lie at the heart of proposals to shape motional mode spectra, simulate quantum magnetism and coherently drive structural phase transitions; in addition we propose using these effects to simulate cosmological particle creation, study quantum fluctuations of work and minimize ion micromotion. Mitigation of Stark effects is important for coherent control of Rydberg ions; we illustrate this by carrying out the first Rabi oscillations between a low-lying electronic state and a Rydberg state of an ion.Although ions in Paul traps are trapped close to electric field nulls, they experience non-zero electric fields which modify the trapping potential via the quadratic Stark effect ∆E = − 1 2 αE 2 . While this modification is small for atomic ions in low-lying electronic (LLE) states, it strongly affects the trapping potential of highlypolarizable Rydberg ions, causing striking phenomena to emerge when trapped ions are excited to Rydberg states.Because the trap stiffness is modified by the Stark effect, atomic transition frequencies depend on motional phonon number and differential polarizabilities. This temperature-dependent Stark shift must be accounted for in trapped ion atomic clocks which operate below the 10 -17 level [1-3]. We observe this effect directly for the first time by exciting an ion to a highly-polarizable Rydberg state.We find that a static offset electric field changes the equilibrium position and the minimum potential of the trapping potential of a highly-polarizable Rydberg ion relative to that of an ion in a LLE state. The change in minimum potential alters the Rydberg-excitation energy; this shift may be used to reduce micromotion beyond the state-of-the-art level. Micromotion minimalization is critical for trapped ion atomic clocks [4, 5] and for studies of atom-ion collisions in the quantum regime [6][7][8]. The change in trap position allows us to strongly drive phonon-number changing transitions during Rydberg excitation. The shifted trapping potential means our system may be used for studying quantum fluctuations of work [9, 10] or for simulations of molecular dynamics [11].Trapped Rydberg ions are an exciting new platform for quantum information processing [12], which combines the exquisite control of trapped ion systems with the strong interactions of Rydberg atoms. Stark effects must be mitigated for Rydberg ions to be coherently controlled; we illustrate this by driving the first Rabi oscillations between a LLE state and a Rydberg...

The existence of ideal quantum measurements is one of the fundamental predictions of quantum mechanics. In theory the measurement projects onto the eigenbasis of the measurement observable while preserving all coherences of degenerate eigenstates. The question arises whether there are dynamical processes in nature that correspond to such ideal quantum measurements. Here we address this question and present experimental results monitoring the dynamics of a naturally occurring measurement process: the coupling of a trapped ion qutrit to the photon environment. By taking tomographic snapshots during the detection process, we show with an average fidelity of 94% that the process develops in agreement with the model of an ideal quantum measurement.