Entanglement-Enhanced Optical Atomic Clocks

Recent developments in atomic physics have enabled the experimental generation of many-body entangled states to boost the performance of quantum sensors beyond the Standard Quantum Limit (SQL). This limit is imposed by the inherent projection noise of a quantum measurement. In this perspective article, we describe the commonly used experimental methods to create many-body entangled states to operate quantum sensors beyond the SQL. In particular, we focus on the potential of applying quantum entanglement to state-of-the-art optical atomic clocks. In addition, we present recently developed time-reversal protocols that make use of complex states with high quantum Fisher information without requiring sub-SQL measurement resolution. We discuss the prospects for reaching near-Heisenberg limited quantum metrology based on such protocols.Comment: 8 pages, 7 figures, perspective articl

Robust kHz-linewidth distributed Bragg reflector laser with optoelectronic feedback

We demonstrate a combination of optical and electronic feedback that significantly narrows the linewidth of distributed Bragg reflector lasers (DBRs). We use optical feedback from a long external fiber path to reduce the high-frequency noise of the laser. An electro-optic modulator placed inside the optical feedback path allows us to apply electronic feedback to the laser frequency with very large bandwidth, enabling robust and stable locking to a reference cavity that suppresses low-frequency components of laser noise. The combination of optical and electronic feedback allows us to significantly lower the frequency noise power spectral density of the laser across all frequencies and narrow its linewidth from a free-running value of 1.1 MHz to a stabilized value of 1.9 kHz, limited by the detection system resolution. This approach enables the construction of robust lasers with sub-kHz linewidth based on DBRs across a broad range of wavelengths.Comment: 5 pages, 3 figure

Increased Atom-Cavity Coupling through Cooling-Induced Atomic Reorganization

The strong coupling of atoms to optical cavities can improve optical lattice clocks as the cavity enables metrologically useful collective atomic entanglement and high-fidelity measurement. To this end, it is necessary to cool the ensemble to suppress motional broadening, and advantageous to maximize and homogenize the atom-cavity coupling. We demonstrate resolved Raman sideband cooling via the cavity as a method that can simultaneously achieve both goals. In 200 ms, we cool 171Yb atoms to an average vibration number = 0.23(7) in the tightly binding direction, resulting in 93% optical {\pi}-pulse fidelity on the clock transition 1S0 -> 3P0. During cooling, the atoms self-organize into locations with maximal atom-cavity-coupling, which will improve quantum metrology applications.Comment: 5 + 2 pages, 5 + 2 figure

Trapping 171^{171}Yb Atoms into a One-Dimensional Optical Lattice with a Small Waist

In most experiments with atoms trapped in optical lattices, the transverse size of the optical lattice beams is on the order of tens of micrometers, and loading many atoms into smaller optical lattices has not been carefully investigated. We report trapping 1500 $^{171}$Yb atoms in a one-dimensional optical lattice generated by a narrow cavity mode at a distance of 0.14 mm from a mirror surface. The simplest approach of loading atoms from a mirror magneto-optical trap overlapped with the cavity mode allows the adjustment of the loading position by tuning a uniform bias magnetic field. The number of atoms trapped in the optical lattice exhibits two local maxima for different lattice depths, with a global maximum in the deeper lattice. These results open a way to quantum mechanical manipulation of atoms based on strong interaction with a tightly focused light field.Comment: 9 pages, 8 figure

Near-Unitary Spin Squeezing in 171^{171}Yb

Spin squeezing can improve atomic precision measurements beyond the standard quantum limit (SQL), and unitary spin squeezing is essential for improving atomic clocks. We report substantial and nearly unitary spin squeezing in $^{171}$Yb, an optical lattice clock atom. The collective nuclear spin of $\sim 10^3$ atoms is squeezed by cavity feedback, using light detuned from the system's resonances to attain unitarity. The observed precision gain over the SQL is limited by state readout to 6.5(4) dB, while the generated states offer a gain of 12.9(6) dB, limited by the curvature of the Bloch sphere. Using a squeezed state within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2). In the future, the squeezing can be simply transferred onto the optical clock transition of $^{171}$Yb.Comment: 5 pages, 4 figure

Improving Metrology with Quantum Scrambling

Quantum scrambling describes the fast spreading of quantum information into many degrees of freedom of a many-body quantum system. This concept embraces many apparently unconnected phenomena such as the thermalization of closed quantum systems, the growth of entanglement, and the black-hole information paradox. The fastest scramblers disperse the information exponentially quickly into the system's degrees of freedom. Out-of-time-order correlators (OTOCs) have been invented as a mean to characterize quantum scrambling. To experimentally probe OTOCs, it is necessary to reverse the sign of the many-body Hamiltonian, effectively evolving the system backwards in time, a technique that has also been shown as powerful for entanglement-enhanced metrology. However, despite experimental progress, to date no exponentially fast scrambling of quantum information has been experimentally demonstrated. Here we probe the exponential scrambling nature of the Lipkin-Meshkov-Glick (LMG) many-body Hamiltonian. We measure an exponentially growing OTOC; moreover, we elucidate and experimentally validate the close conceptual relation between quantum information scrambling and quantum-enhanced metrology. Our experiment paves the way to the investigation of quantum chaos and scrambling in controlled tabletop experiments. Moreover, we demonstrate that entanglement-enhanced quantum metrology can be performed with general fast-scrambling Hamiltonians capable of generating entanglement exponentially quickly.Comment: 6 pages, 5 figure

Geometrically asymmetric optical cavity for strong atom-photon coupling

Optical cavities are widely used to enhance the interaction between atoms and light. Typical designs using a geometrically symmetric structure in the near-concentric regime face a tradeoff between mechanical stability and high single-atom cooperativity. To overcome this limitation, we design and implement a geometrically asymmetric standing-wave cavity. This structure, with mirrors of very different radii of curvature, allows strong atom-light coupling while exhibiting good stability against misalignment. We observe effective cooperativities ranging from $\eta_{\rm eff}=10$ to $\eta_{\rm eff}=0.2$ by shifting the location of the atoms in the cavity mode. By loading $^{171}$Yb atoms directly from a mirror magneto-optical trap into a one-dimensional optical lattice along the cavity mode, we produce atomic ensembles with collective cooperativities up to $N\eta=2\times 10^4$. This system opens a way to preparing spin squeezing for an optical lattice clock and to accessing a range of nonclassical collective states.Comment: 8 pages, 7 figures, published versio

Producção de um Condensado de Bose-Einstein de átomos de sódio e investigação considerando interações não lineares entre átomos e fótons

In this work we constructed an experimental system to realize a BEC of sodium atoms. In the first part of the work, we study two atomic sources in order to choose the most suitable for our system. The comparison between a Zeeman slower and a bidimensional magnetooptical trap (2D-MOT) was performed to evaluate the capacity of producing an appropiate flux of atoms in order to load a tridimensional magneto-optical trap (3D-MOT). The experimental results show that the 2D-MOT is as efficient as the Zeeman slower with the advantage of being more compact and easier to operate, and for these reasons we choose it as our source of cold atoms. After this, the experimental apparatus to produce a Bose-Einstein condensate was constructed and characterized. With this experimental system we realized all the required stages to achieve the Bose-Einstein condensation (BEC). Initially, we characterized and compared the performance between the Bright-MOT and Dark-SPOT MOT of sodium atoms, observing the great advantages this last configuration offers. Afterward, we implemented the experimental sequence for the achivement of the BEC of sodium atoms. After the optical molasses process, the atoms are tranferred to an optically plugged quadrupole trap (OPT) where the process of evaporative cooling is performed. With this setup, we achive a sodium BEC with ∼ 5×105 atoms and a critical temperature of ∼ 1.1 μK. Finally, with the constructed and characterized machine, we started to perform experiments of cooperative absorption of two photons by two trapped atoms. With the new system, we wanted to take advantage of the higher densities in the magnetic trap and BEC to explore some features of this phenomenon in the classical and quantum regimes. We were interested in exploring some features of this nonlinear light-matter interaction effect. The idea of having two or more photons interacting with two or more atoms is the beginning of a new possible class of phenomena that we could call many photons-many body intercation. In this new possibity, photons and atoms will be fully correlated, introducing new aspects of interactions.Neste trabalho, realizamos a construção de um sistema experimental para a realização de um condensado de Bose-Einstein de átomos de sódio. Na primeira parte do trabalho, realizamos o estudo de duas fontes átomicas com o intuito de escolher a mais adequada para nosso sistema experimental. A comparação foi realizada entre um Zeeman slower e uma armadilha magneto-óptica bidimensional (MOT-2D), que são técnicas usadas para fornecer um grande fluxo de átomos com distribuição de velocidades adequadas para serem capturados numa armadilha magneto-óptica tridimensional (MOT-3D). Os resultados experimentais da caracterização de ambos os sistemas mostra que o MOT-2D oferece um grande fluxo atômico da mesma ordem do Zeeman slower, mas com a vantagem de ser um sistema mais compacto em questão de tamanho, razão pela qual foi escolhido como fonte atômica no nosso sistema. A partir daqui, realizamos a construção do sistema experimental para a realização do condensado de sódio. Inicialmente realizamos o aprisionamento numa MOT-3D, realizando subsequentemente os passos de resfriamento sub-Doppler mediante o processo de molasses ópticas. Depois disto, os átomos são transferidos para uma armadilha magnética, que consiste de um par de bobinas em configuração anti-Helmholtz, as mesmas usadas para a MOT-3D mas com um gradiente de campo magnético ao redor de uma ordem de grandeza maior. Esta armadilha é combinada com um laser com dessintonia para o azul focado a 30 μm no centro da armadilha, onde o campo magnético é zero com o objetivo de evitar as perdas por majorana que acontecem nessa região. Com esta configuração, um condensado de ∼ 5 × 105 átomos é obtido a uma temperatura crítica de ∼ 1.1 μK. Por último, com a máquina construída e caracterizada, começamos re-explorar o experimento de absorção cooperativa de dois fótons por dois átomos aprisionados. Com nosso novo sistema, é possível explorar este efeito no regime clássico e quântico. Estamos interessados em explorar algumas características da interação não linear entre luz e matéria. A ideia de ter dois ou mais fótons interagindo com um ou mais átomos, é possivelmente o começo de uma nova classe de fenômenos que poderíamos chamar de interação de muitos fótons com muitos átomos

Cooperative absorption of two-photon in cold atoms

Neste trabalho estudamos a absorção cooperativa de dois fótons em processos de colisão entre átomos frios de sódio aprisionados. Efeitos não-lineares exigem amostras de alta densidade para ser observados. Redesenhamos nosso sistema experimental para conseguir amostras de 1012 átomos/cm3. As principais alterações foram a construção de um desacelerador Zeeman em configuração spin-flip, a implementação de bombeamento diferencial entre o forno e a câmara principal, assim como redesenhar o forno. A fim de compreender e melhorar os processos de medição utilizamos a técnica de fotoionização nos estados 32P1/2 e 32P3/2. Com esses dados conseguimos calcular a seção transversal de ionização para cada um desses estados, que está de acordo com valores reportados na literatura. Estes resultados mostram que o novo desenho do sistema permite um grande ponto de partida para a medição da absorção de dois fótons. Uma tentativa de medir a absorção de dois fótons foi feita. Um pequeno aumento no número de íons produzidos por unidade de tempo foi observada em uma região deslocada para o vermelho de cerca de 4,5 GHz de onde inicialmente se esperava ocorrer a transição. Isto motiva a aprofundar o estudo da absorção de dois fótons, já que provavelmente essa medida seja um indício da ocorrência desse fenômeno. Assim, tanto a medição da seção de choque dos estados 32P1/2 e 32P3/2 e a tentativa de medir a absorção de dois fótons, fornecem uma base sólida para conhecer qual é a melhor maneira de obter resultados mais decisivos no que diz respeito à absorção cooperativa de dois fótons, e as vantagens do nosso sistema em futuros experimentos.In this work we study the cooperative two-photon absorption in collisional processes between cold trapped sodium atoms. Nonlinear effects require high density samples to be observed. We redesign our experimental system to achieve samples up to 1012 atoms/ cm3 .The key changes were building a spin-flip Zeeman slower, implementing differential pumping between the oven and the chamber and changing the oven´s design. In order to understand and improve the measurement processes we did photoionization from the states 32P1/2 e 32P3/2. With this data we could calculate the ionization cross section for each of these states, which is in agreement with values reported in the literature. These results show that the new design of the system allows a great starting point for measuring of two-photon absorption. An attempt to measure the absorption of two-photon was made. A small increase in the number of ions produced per unit time was observed in a region shifted to the red of about 4.5 GHz from where we initially expected the transition to occur. This probably indicates two-photon absorption. Thus, both the measurement of cross section of states and the attempt to measure the absorption of two photons, provide a solid foundation for understanding what is the best way to obtain more decisive results with regard to cooperative absorption, and the advantages of performance of our system in future experiments