Qubits encoded in the electronic states of single atoms trapped in arrays of optical tweezers are a promising platform for a universal quantum computer. These qubits can be prepared in a well-defined quantum state, coherently manipulated using a nearresonant driving field, and their state detected with high fidelity. The most promising aspect of this platform is the large scalability, with arrays of up to 6100 qubits demonstrated[62].We present our progress in developing such a system with an array of single 85Rbatoms. We provide an overview of the experimental setup constructed for this purpose. Typically 50 atoms are loaded from a MOT into a 10×10 array of optical tweezers with sub-micrometer waists, with only a single atom present in a tweezer. The occupation of the tweezers is determined using a fluorescence image. We provide a characterisation of the trapping potentials experienced by the atoms. This characterisation is performed by measuring properties of the atoms in the tweezers, allowing for an in situ characterisation. In particular, the trap depth and trap frequencies were characterised. The temperature of the atoms after the initial fluorescence image was determined using the release and recapture technique [101] and the trapping lifetime of the atom was measured. With the ability to prepare, manipulate, and read out the electronic state of the atoms, an array of hyperfine qubits has been created. The qubits are encoded in the hyperfine clock states as |0⟩ := 52S1/2 |F = 2,mF = 0⟩ and |1⟩ := 52S1/2 |F = 3,mF = 0⟩. These long-lived first-order Zeeman shift insensitive states exhibit good coherence times, which we have characterized as T1=205 ± 3 ms , T2* = 2.01 ± 0.02 ms, andT2 echo = 67.1 ± 0.1 ms. State preparation is achieved by repetitions of optical and microwave pulses, to which the |0⟩ state is dark, allowing for population to accumulate in this state. The coherent evolution of the qubits have been performed using 3.035 GHz microwave radiation. The antenna used to produce this radiation is a home-built fullwave loop antenna. The antenna has allowed for addressing the qubits with Rabi frequencies up to Ω/2π ≈ 160 kHz. We have implemented the single-qubit Clifford gates using the global microwave drive. We determine using randomized benchmarking an166 Summary average gate fidelity of 0.99949(3), limited by Rabi frequency inhomogeneity over the array. To combat this fidelity limitation, we repeated the randomized benchmarking using the pulse length error robust SCROFULOUS pulses [135], which resulted in an increased gate fidelity of 0.999653(5). As a further extension of the capabilities of the system, we demonstrated a preliminary implementation of addressing a single atom int he array by applying a local Rz rotation to the selected qubit using a Stark shifting laser. The high level of control of the microwave radiation has allowed for an experimental verification of control noise-fidelity relations proposed by [115]. We have found good agreement between the experimentally measured fidelities and the proposed analytical relations developed using the stochastic Schrödinger equation. As a preliminary step towards implementing a two-qubit gate, we have performed coherent excitation of the |1⟩ state to the |r ⟩ :=602S1/2 |mJ = −1/2> Rydberg state using an off-resonant two-photon excitation. The low contrast of the Rabi oscillations on the |1⟩↔|r ⟩ transition was investigated using a simple Lindblad master equation based model. The largest contributors to the reduced contrast is SPAM error, intermediate state scattering and laser phase noise. Since Rydberg atoms interact via the van der Waals interaction, the spacing between atoms must be deterministically controlled. For this purpose, we have used an additional optical tweezer which can be dynamically moved using an acousto-optic deflector to rearrange the stochastically filled array into a desired configuration. By placing 2 atoms a distance ≈ 5 μm apart, we have demonstrated the p2 enhancement of the Rabi oscillation on the |1⟩↔|r ⟩ transition, a required first step towards implementing an entangling gate between the hyperfine qubits. To extend the temperature-limited T2* coherence time, we have implemented Λ-enhanced gray molasses cooling. We have opted to perform this cooling on the D2line as it is experimentally convenient to use this transition. Because using this transition for this purpose has not been reported in this isotope of Rb, we studied the efficacy of this cooling scheme under these circumstances. The reduced excited state hyperfine splitting of 85Rb compared to 87Rb has allowed for the study of the efficacy of this technique in the presence of additional transitions that may inhibit the cooling performance. Despite the challenges of the smaller hyperfine splitting, we have cooled the atoms to4.0±0.2 μK. This additional cooling is partially negated by the heating from the qubit state preparation procedure, but the additional cooling has allowed for the average T2*to be extended from ⟨T2*⟩ = 3.4 ± 0.1 ms to ⟨T2*⟩ = 5.3 ± 0.2 ms.
Qubits encoded in the electronic states of single atoms trapped in arrays of optical tweezers are a promising platform for a universal quantum computer. These qubits can be prepared in a well-defined quantum state, coherently manipulated using a nearresonant driving field, and their state detected with high fidelity. The most promising aspect of this platform is the large scalability, with arrays of up to 6100 qubits demonstrated[62].We present our progress in developing such a system with an array of single 85Rbatoms. We provide an overview of the experimental setup constructed for this purpose. Typically 50 atoms are loaded from a MOT into a 10×10 array of optical tweezers with sub-micrometer waists, with only a single atom present in a tweezer. The occupation of the tweezers is determined using a fluorescence image. We provide a characterisation of the trapping potentials experienced by the atoms. This characterisation is performed by measuring properties of the atoms in the tweezers, allowing for an in situ characterisation. In particular, the trap depth and trap frequencies were characterised. The temperature of the atoms after the initial fluorescence image was determined using the release and recapture technique [101] and the trapping lifetime of the atom was measured. With the ability to prepare, manipulate, and read out the electronic state of the atoms, an array of hyperfine qubits has been created. The qubits are encoded in the hyperfine clock states as |0⟩ := 52S1/2 |F = 2,mF = 0⟩ and |1⟩ := 52S1/2 |F = 3,mF = 0⟩. These long-lived first-order Zeeman shift insensitive states exhibit good coherence times, which we have characterized as T1=205 ± 3 ms , T2* = 2.01 ± 0.02 ms, andT2 echo = 67.1 ± 0.1 ms. State preparation is achieved by repetitions of optical and microwave pulses, to which the |0⟩ state is dark, allowing for population to accumulate in this state. The coherent evolution of the qubits have been performed using 3.035 GHz microwave radiation. The antenna used to produce this radiation is a home-built fullwave loop antenna. The antenna has allowed for addressing the qubits with Rabi frequencies up to Ω/2π ≈ 160 kHz. We have implemented the single-qubit Clifford gates using the global microwave drive. We determine using randomized benchmarking an166 Summary average gate fidelity of 0.99949(3), limited by Rabi frequency inhomogeneity over the array. To combat this fidelity limitation, we repeated the randomized benchmarking using the pulse length error robust SCROFULOUS pulses [135], which resulted in an increased gate fidelity of 0.999653(5). As a further extension of the capabilities of the system, we demonstrated a preliminary implementation of addressing a single atom int he array by applying a local Rz rotation to the selected qubit using a Stark shifting laser. The high level of control of the microwave radiation has allowed for an experimental verification of control noise-fidelity relations proposed by [115]. We have found good agreement between the experimentally measured fidelities and the proposed analytical relations developed using the stochastic Schrödinger equation. As a preliminary step towards implementing a two-qubit gate, we have performed coherent excitation of the |1⟩ state to the |r ⟩ :=602S1/2 |mJ = −1/2> Rydberg state using an off-resonant two-photon excitation. The low contrast of the Rabi oscillations on the |1⟩↔|r ⟩ transition was investigated using a simple Lindblad master equation based model. The largest contributors to the reduced contrast is SPAM error, intermediate state scattering and laser phase noise. Since Rydberg atoms interact via the van der Waals interaction, the spacing between atoms must be deterministically controlled. For this purpose, we have used an additional optical tweezer which can be dynamically moved using an acousto-optic deflector to rearrange the stochastically filled array into a desired configuration. By placing 2 atoms a distance ≈ 5 μm apart, we have demonstrated the p2 enhancement of the Rabi oscillation on the |1⟩↔|r ⟩ transition, a required first step towards implementing an entangling gate between the hyperfine qubits. To extend the temperature-limited T2* coherence time, we have implemented Λ-enhanced gray molasses cooling. We have opted to perform this cooling on the D2line as it is experimentally convenient to use this transition. Because using this transition for this purpose has not been reported in this isotope of Rb, we studied the efficacy of this cooling scheme under these circumstances. The reduced excited state hyperfine splitting of 85Rb compared to 87Rb has allowed for the study of the efficacy of this technique in the presence of additional transitions that may inhibit the cooling performance. Despite the challenges of the smaller hyperfine splitting, we have cooled the atoms to4.0±0.2 μK. This additional cooling is partially negated by the heating from the qubit state preparation procedure, but the additional cooling has allowed for the average T2to be extended from ⟨T2⟩ = 3.4 ± 0.1 ms to ⟨T2*⟩ = 5.3 ± 0.2 ms.
Optical tweezer arrays of neutral atoms have emerged as a versatile and powerful platform for quantum simulation and quantum information processing. In this thesis, I present the realization of an experimental platform for quantum simulation based on individually trapped strontium atoms in optical tweezer arrays. The experiment combines precise laser cooling, optical control, and high-resolution imaging to enable the manipulation and high fidelity detection of single atoms. I developed and optimized a two-stage three-dimensional magneto-optical trap (3D-MOT) that produces cold and dense samples of strontium atoms from a thermal beam. In the f irst stage, atoms are captured and precooled using the dipole-allowed 1S0 → 1P1 transition at 461nm (which has a linewidth of !=2ω ↑ 32MHz). The second stage employs the 1S0 → 3P1 narrow intercombination transition at 689nm (with a linewidth of !=2ω ↑7.5kHz) to further cool and compress the atomic cloud. By optimizing the trapping parameters, I achieved clouds with temperatures around 5μK and densities above 1010cm→3, providing ideal initial conditions for e!cient loading into optical tweezers. A 3↑3 array of 360μK deep optical tweezers is generated by spatially modulating an 813.4nm laser beam using two crossed acousto-optic deflectors. The deflected beams are relayed and focused into the science chamber using a high–numericalaperture objective, which simultaneously serves as the collection optics for atomic f luorescence. The fluorescence light emitted by the atoms is imaged onto a scientific qCMOS camera, enabling site-resolved detection of individual atoms. I implemented and optimized the in-trap cooling dynamics to prevent atom loss during imaging and to minimize residual thermal motion. In addition, by precisely tuning lightassisted collisions, multiple atoms occupancies are removed from the traps and a single-atom regime is reached in the array, with a filling fraction of about 50%. I have demonstrated a single-atom detection fidelity of 99,986(1)% and a survival probability of 97(2)% between subsequent image acquisition, comparable to other current state-of-the-art experiments. To characterize the platform, I carried out release-and-recapture experiments, from which it is possible to measure a temperature for the individually trapped atoms of 12.95(5)μK. These results demonstrate the successful implementation of a robust and high-fidelity platform for optical trapping and imaging of single strontium atoms. The apparatus provides the foundation for future quantum simulation experiments with alkalineearth atoms excited to the Rydberg state, o"ering precise control over individual particles and the ability to scale towards larger, programmable atomic arrays.
Abstract The results of experiments on the implementation of single-qubit quantum gates with a single 87Rb atom in an optical dipole trap with a wavelength of 850 nm are presented. The trap is formed by a long focal-length objective lens located outside the vacuum chamber of a magneto-optical trap. An atom is detected using a resonance fluorescence signal with an sCMOS video camera. The experiments involved the trapping and confinement of a single atom at times up to 50 s, optical pumping by polarized laser radiation, microwave transitions between two hyperfine sublevels of the ground state, and the measurement of the quantum state of the atom by pushing it from the trap. Rabi oscillations are observed during the “clock” microwave transition 5S1/2(F = 2, MF = 0) → 5S1/2(F = 1, MF = 0) between two operating qubit levels at a frequency of up to 4.2 kHz, a contrast of up to 95%, and a coherence time of up to 3 ms. These oscillations correspond to the implementation of two basic single-qubit quantum operations (Hadamard gate, NOT gate) from various initial qubit states with an average fidelity of 95.2 ± 3%.
We report on the realization of a platform for trapping and manipulating individual 88Sr atoms in optical tweezers. A first cooling stage based on a blue shielded magneto-optical trap (MOT) operating on the |1S0⟩→|1P1⟩ transition at 461 nm enables us to trap approximately 4 × 106 atoms at a temperature of 6.8 mK. Further cooling is achieved in a narrow-line red MOT using the |1S0⟩→|3P1⟩ intercombination transition at 689 nm, bringing 5 × 105 atoms down to 5μK and reaching a density of 4 × 1010 cm3. Atoms are then loaded into 813 nm tweezer arrays generated by crossed acousto-optic deflectors and tightly focused onto the atoms with a high-numerical-aperture objective. Through light-assisted collision processes we achieve the collisional blockade, which leads to single-atom occupancy with a probability of about 50%. The trapped atoms are detected via fluorescence imaging with a fidelity of 99.986(6)%, while maintaining a survival probability of 97(2)%. The release-and-recapture measurement provides a temperature of 12.92(5)μK for the atoms in the tweezers, and the ultra-high-vacuum environment ensures a vacuum lifetime higher than 7 min. These results demonstrate a robust alkaline-earth tweezer platform that combines efficient loading, cooling, and high-fidelity detection, providing the essential building blocks for scalable quantum simulation and quantum information processing with Sr atoms.
Optical tweezer arrays 1,2 have transformed atomic and molecular physics, now forming the backbone for a range of leading experiments in quantum computing 3–8 , simulation 1,9–12 , and metrology 13–15 . Typical experiments trap tens to hundreds of atomic qubits, and recently systems with around one thousand atoms were realized without defining qubits or demonstrating coherent control 16–18 . However, scaling to thousands of atomic qubits with long coherence times, low-loss, and high-fidelity imaging is an outstanding challenge and critical for progress in quantum science, particularly towards quantum error correction 19,20 . Here, we experimentally realize an array of optical tweezers trapping over 6,100 neutral atoms in around 12,000 sites, simultaneously surpassing state-of-the-art performance for several metrics that underpin the success of the platform. Specifically, while scaling to such a large number of atoms, we demonstrate a coherence time of 12.6(1) seconds, a record for hyperfine qubits in an optical tweezer array. We show room-temperature trapping lifetimes of ~ 23 minutes, enabling record-high imaging survival of 99.98952(1)% with an imaging fidelity of over 99.99%. We present a plan for zone-based quantum computing 5,21 and demonstrate necessary coherence-preserving qubit transport and pick-up/drop-off operations on large spatial scales, characterized through interleaved randomized benchmarking. Our results, along with recent developments 8,22–24 , indicate that universal quantum computing and quantum error correction with thousands to tens of thousands of physical qubits could be a near-term prospect.
Quantum simulation offers the possibility to study quantum mechanical problems which are untraceable on classical computers. This thesis introduces a novel platform for quantum simulation and presents the first experimental realisation of single potassium atoms trapped in optical tweezers. Interactions between individual atoms are induced by strong energy shifts of atoms excited to states with large principal quantum number, so-called Rydberg states. Either direct excitation to Rydberg states or off-resonant dressing can be used to induce these interactions. We argue that potassium is well-suited for the implementation of Rydberg dressing, enabling simultaneous dressing of both ground states to engineer complex interactions. Using techniques to cool and trap cold atoms, single potassium atoms are prepared in arrays of optical tweezers. Raman sideband cooling reduces vibrational excitations and prepares the atoms close to the motional ground state. This cooling technique mitigates severe limitations for Rydberg dressing, arising from thermal broadening and inhomogeneous light shifts in the array of atoms. To directly excite atoms to Rydberg states, a high power laser setup with two cavity-enhanced frequency doubling stages is constructed, generating up to one Watt of ulta-violet light at 286 nm. By exciting atoms to Rydberg states we observe Rabi oscillations with Rabi frequencies of up to 1 MHz, demonstrating coherent control of Rydberg atoms. Finally, we combine these techniques to observe interactions in two ways: First, we create a so-called superatom of up to four individual atoms using direct excitation and Rydberg-blockade and observe coherent oscillations to this collective state. We measure the expected square root scaling of the effective Rabi frequency with the number of individual atoms, confirming the creation of a many-body entangled state. Secondly, we off-resonantly dress the atoms prepared in a one-dimensional chain and measure correlated interaction shifts over multiple sites. In summary, we have developed a platform for quantum simulation with single atoms in optical tweezers. The presented results show coherent control of single atoms and interactions induced by Rydberg states. We have thus demonstrated that the system is well-suited for quantum simulation of many-body systems.
Neutral atoms trapped and manipulated by laser light provide experimentally well accessible quantum systems allowing for a high degree of control over external and internal degrees of freedom. Arrays of dipole traps in which the atoms are confined individually in a configurable geometry constitute a versatile platform for quantum simulation and information applications. By exciting these atoms into Rydberg states, interactions of variable strength and range can be introduced into the system, allowing for the implementation of entangling gate operations or spin Hamiltonians. A crucial requirement for these schemes to function in a reliable way is the ability to create defect-free arrays of single atoms. This is generally a challenge in these types of systems, as common atom loading schemes are limited to roughly 50% probability of filling each site. In this work, a technique for the rearrangement of atoms within a scalable architecture based on micro-optical lens arrays was developed and implemented, resulting in the creation of uniformly filled regions containing more than 100 atoms, which represent the largest defect-free structures realized so far in systems of this kind. This was accomplished by filling the empty traps in a pre-defined pattern with an atom one by one using an optical tweezer. Thus, structures with up to 5 x 5 atoms could be rendered defect-free in more than 99% of attempts. Although the success rate drops below unity for larger clusters, a value of 3.1% for a 100-atom structure is still viable for experiments working with post-selection methods. The filling fraction of even the largest examined structures was observed to be higher than 88%, surpassing common loading schemes by a significant margin. The measurements presented in this thesis build on a region of the array containing 361 sites, being limited by available laser power. In contrast, the addressable range of the optical tweezer includes more than 1500 sites and microlens arrays with up to a million lenses are commercially available. By implementing coherent Rydberg excitation of this assembled atom array, significant progress toward a universal quantum computer or flexible quantum simulator has been made. Using a two-photon excitation scheme, coherent dynamics between the ground and Rydberg state could be observed simultaneously in a 5 x 5 region of the array, with two-photon Rabi frequencies on the order of Omega = 2Pi x 500kHz measured for a Rydberg laser beam waist of w_0,B = 18.7(10) µm. The choice of an appropriate Rydberg state and interatomic spacing led to the presence of strong nearest-neighbor interactions and allowed for the demonstration of the Rydberg blockade effect by observing a collective enhancement of the Rabi frequency consistent with the expected scaling ~ sqrt(N) as well as the suppression of multiple excitations. This mechanism represents the fundamental constituent of a two-qubit gate operation. The architecture introduced in this work offers a scalability unique among quantum simulation platforms and the presented results underpin its potential to propel the atom-optical approach for quantum information processing beyond the threshold of quantum supremacy. Different approaches for scaling up the system have been explored, indicating that defect-free structures of more than 1000 atoms are within range with feasible experimental improvements. Through a detailed analysis of the factors limiting the coherence of the observed dynamics, strategies for future experimental improvements have been developed. Among these, increasing the coupling strength to the Rydberg state into the megahertz regime by increasing laser power and implementing single-site addressing represents the most straight-forward and promising approach.