Two-photon Raman Process Research Articles

Resolved Raman sideband cooling of a single optically trapped cesium atom.

We developed a resolved Raman sideband cooling scheme that can efficiently prepare a single optically trapped cesium (Cs) atom in its motional ground states. A two-photon Raman process between two outermost Zeeman sublevels in a single hyperfine state is applied to reduce the phonon number. Our scheme is less sensitive to the variation in the magnetic field than the commonly used scheme where the two outermost Zeeman sublevels belonging to the two separate ground hyperfine states are taken. Fast optical pumping with less spontaneous emission guarantees the efficiency of the cooling process. After cooling for 50 ms, 82% of the Cs atoms populate their three-dimensional ground states. Our scheme improves the long-term stability of Raman sideband cooling in the presence of magnetic field drift and is thus suitable for cooling other trapped atoms or ions with abundant magnetic sublevels.

Nonequilibrium phases of ultracold bosons with cavity-induced dynamic gauge fields

Gauge fields are a central concept in fundamental theories of physics, and responsible for mediating long-range interactions between elementary particles. Recently, it has been proposed that dynamical gauge fields can be naturally engineered by photons in composite, neutral quantum gas-cavity systems using suitable atom-photon interactions. Here we comprehensively investigate nonequilibrium dynamical phases appearing in a two-leg bosonic lattice model with leg-dependent, dynamical complex tunnelings mediated by cavity-assisted two-photon Raman processes. The system constitutes a minimal dynamical flux-lattice model. We study fixed points of the equations of motion and their stability, the resultant dynamical phase diagram, and the corresponding phase transitions and bifurcations. Notably, the phase diagram features a plethora of nonequilibrium dynamical phases including limit-cycle and chaotic phases. In the end, we relate regular periodic dynamics (i.e., limit-cycle phases) of the system to time crystals.

Dispersive optical systems for scalable Raman driving of hyperfine qubits

Hyperfine atomic states are among the most promising candidates for qubit encoding in quantum information processing. In atomic systems, hyperfine transitions are typically driven through a two-photon Raman process by a laser field which is amplitude modulated at the hyperfine qubit frequency. Here, we introduce a new method for generating amplitude modulation by phase modulating a laser and reflecting it from a highly dispersive optical element known as a chirped Bragg grating (CBG). This approach is passively stable, offers high efficiency, and is compatible with high-power laser sources, enabling large Rabi frequencies and improved quantum coherence. We benchmark this new approach by globally driving an array of $\sim 300$ neutral $^{87}$Rb atomic qubits trapped in optical tweezers, and obtain Rabi frequencies of 2 MHz with photon-scattering error rates of $< 2 \times 10^{-4}$ per $\pi$-pulse. This robust approach can be directly integrated with local addressing optics in both neutral atom and trapped ion systems to facilitate high-fidelity single-qubit operations for quantum information processing.

Bose–Einstein condensates under a non-Hermitian spin–orbit coupling* *Project supported by the National Natural Science Foundation of China (Grant No. 11974331).

We study the properties of Bose–Einstein condensates under a non-Hermitian spin–orbit coupling (SOC), induced by a dissipative two-photon Raman process. We focus on the dynamics of the condensate at short times, when the impact of decoherence induced by quantum jumps is negligible and the dynamics is coherently driven by a non-Hermitian Hamiltonian. Given the significantly modified single-particle physics by dissipative SOC, the interplay of non-Hermiticity and interaction leads to a quasi-steady-state phase diagram different from its Hermitian counterpart. In particular, we find that dissipation can induce a phase transition from the stripe phase to the plane-wave phase. We further map out the phase diagram with respect to the dissipation and interaction strengths, and finally investigate the stability of quasi-steady states through the time-dependent dissipative Gross–Pitaevskii equation. Our results are readily accessible based on standard experiments with synthetic spin–orbit couplings.

Dissipation-facilitated molecules in a Fermi gas with non-Hermitian spin-orbit coupling

We study the impact of non-Hermiticity on the molecule formation in a two-component spin-orbit-coupled Fermi gas near a wide Feshbach resonance. Under an experimentally feasible configuration where the two-photon Raman process is dissipative, the Raman-induced synthetic spin-orbit coupling acquires a complex strength. Remarkably, dissipation of the system facilitates the formation and binding of molecules, which, despite their dissipative nature and finite lifetime, exist over a wider parameter regime than in the corresponding Hermitian system. These dissipation-facilitated molecules can be probed by the inverse radio-frequency (rf) spectroscopy, provided the Raman lasers are blue detuned to the excited state. The effects of dissipation manifest in the rf spectra as shifted peaks with broadened widths, which serve as a clear experimental signature. Our results, readily observable in current cold-atom experiments, shed light on the fascinating interplay of non-Hermiticity and interaction in few- and many-body open quantum systems.

Enhanced transport of spin-orbit-coupled Bose gases in disordered potentials.

Anderson localization is a single-particle localization phenomena in disordered media that is accompanied by an absence of diffusion. Spin-orbit coupling (SOC) describes an interaction between a particle's spin and its momentum that directly affects its energy dispersion, for example, creating dispersion relations with gaps and multiple local minima. We show theoretically that combining one-dimensional spin-orbit coupling with a transverse Zeeman field suppresses the effects of disorder, thereby increasing the localization length and conductivity. This increase results from a suppression of backscattering between states in the gap of the SOC dispersion relation. Here, we focus specifically on the interplay of disorder from an optical speckle potential and SOC generated by two-photon Raman processes in quasi-one-dimensional Bose-Einstein condensates. We first describe backscattering by using a Fermi golden rule approach, and then numerically confirm this picture by solving the time-dependent one-dimensional Gross-Pitaevskii equation for a weakly interacting Bose-Einstein condensate with SOC and disorder. We find that on the tens of millisecond timescale of typical cold atom experiments moving in harmonic traps, initial states with momentum in the zero-momentum SOC gap evolve with negligible backscattering, while without SOC these same states rapidly localize.

Current-assisted Raman activation of the Higgs mode in superconductors

The Higgs mode in superconductors is a scalar mode without electric or magnetic dipole moment. Thus, it is commonly believed that its excitation is restricted to a nonlinear two-photon Raman process. However, recent efforts have shown that a linear excitation in the presence of a supercurrent is possible, resulting in a new resonant enhancement at $\Omega=2\Delta$ with the driving light frequency $\Omega$ and the energy of the Higgs mode $2\Delta$. This is in contrast to the usual $2\Omega = 2\Delta$ resonance condition found in nonlinear third-harmonic generation experiments. In this communication, we show that such a linear excitation can still be described as an effective Raman two-photon process, with one photon at $\omega=2\Delta$ and one virtual photon at $\omega=0$ which represents the dc supercurrent. At the same time we demonstrate that a straightforward infrared activation with a single photon excitation is negligible. Moreover, we give a general context to our theory, providing an explanation for how the excitation of the Higgs mode in both THz quench and drive experiments can be understood within a conventional difference-frequency generation or sum-frequency generation process, respectively. In such a picture, the observed new resonance condition $\Omega = 2\Delta$ is just a special case. With the same approach, we further discuss another recent experiment, where we find a suppression of odd order higher harmonics in the presence of a dc supercurrent.

Optical spin locking of a solid-state qubit

Quantum control of solid-state spin qubits typically involves pulses in the microwave domain, drawing from the well-developed toolbox of magnetic resonance spectroscopy. Driving a solid-state spin by optical means offers a high-speed alternative, which in the presence of limited spin coherence makes it the preferred approach for high-fidelity quantum control. Bringing the full versatility of magnetic spin resonance to the optical domain requires full phase and amplitude control of the optical fields. Here, we imprint a programmable microwave sequence onto a laser field and perform electron spin resonance in a semiconductor quantum dot via a two-photon Raman process. We show that this approach yields full SU(2) spin control with over 98 %pi-rotation fidelity. We then demonstrate its versatility by implementing a particular multi-axis control sequence, known as spin locking. Combined with electron-nuclear Hartmann–Hahn resonances which we also report in this work, this sequence will enable efficient coherent transfer of a quantum state from the electron spin to the mesoscopic nuclear ensemble.

Microscopic theory of cavity-enhanced single-photon emission from optical two-photon Raman processes

We consider cavity-enhanced single-photon generation from stimulated two-photon Raman processes in three-level systems. We compare four fundamental system configurations, one $\Lambda$-, one V- and two ladder ($\Xi$-) configurations. These can be realized as subsystems of a single quantum dot or of quantum-dot molecules. For a new microscopic understanding of the Raman process, we analyze the Heisenberg equation of motion applying the cluster-expansion scheme. Within this formalism an exact and rigorous definition of a cavity-enhanced Raman photon via its corresponding Raman correlation is possible. This definition for example enables us to systematically investigate the on-demand potential of Raman-transition-based single-photon sources. The four system arrangements can be divided into two subclasses, $\Lambda$-type and V-type, which exhibit strongly different Raman-emission characteristics and Raman-emission probabilities. Moreover, our approach reveals whether the Raman path generates a single photon or just induces destructive quantum interference with other excitation paths. Based on our findings and as a first application, we gain a more detailed understanding of experimental data from the literature. Our analysis and results are also transferable to the case of atomic three-level-resonator systems, and can be extended to more complicated multi-level schemes.

Formation of a molecular ion by photoassociative Raman processes

We show theoretically that it is possible to form a cold molecular ion from a pair of colliding atom and ion at low energy by photoassociative two-photon Raman processes. We explore the possibility of stimulated Raman adiabatic passage from the continuum of ion–atom scattering states to an ionic molecular state. We provide physical conditions under which coherent population transfer is possible in stimulated Raman photoassociation. Our results are important for experimental realization of PA in ion–atom cold collisions.

Creation of an Ultracold Gas of Ground-State Dipolar ^{23}Na^{87}Rb Molecules.

We report the successful production of an ultracold sample of absolute ground-state ^{23}Na^{87}Rb molecules. Starting from weakly bound Feshbach molecules formed via magnetoassociation, the lowest rovibrational and hyperfine level of the electronic ground state is populated following a high-efficiency and high-resolution two-photon Raman process. The high-purity absolute ground-state samples have up to 8000 molecules and densities of over 10^{11} cm^{-3}. By measuring the Stark shifts induced by external electric fields, we determined the permanent electric dipole moment of the absolute ground-state ^{23}Na^{87}Rb and demonstrated the capability of inducing an effective dipole moment over 1D. Bimolecular reaction between ground-state ^{23}Na^{87}Rb molecules is endothermic, but we still observed a rather fast decay of the molecular sample. Our results pave the way toward investigation of ultracold molecular collisions in a fully controlled manner and possibly to quantum gases of ultracold bosonic molecules with strong dipolar interactions.

Raman fingerprints on the Bloch sphere of a spinor Bose–Einstein condensate

We explore the geometric interpretation of a diabatic, two-photon Raman process as a rotation on the Bloch sphere for a pseudo-spin- system. The spin state of a spin- quantum system can be described by a point on the surface of the Bloch sphere, and its evolution during a Raman pulse is a trajectory on the sphere determined by properties of the optical beams: the pulse area, the relative intensities and phases and the relative frequencies. We experimentally demonstrate key features of this model with a Rb spinor Bose–Einstein condensate, which allows us to examine spatially dependent signatures of the Raman beams. The two-photon detuning allows us to precisely control the spin density and imprinted relative phase profiles, as we show with a coreless vortex. With this comprehensive understanding and intuitive geometric interpretation, we use the Raman process to create and tailor as well as study and characterize exotic topological spin textures in spinor BECs.

Spin-orbit coupled ultracold gases in optical lattices: High-band physics and insufficiency of tight-binding models

We study the interplay effect of spin-orbit coupling(SOC) and optical lattice to the single-particle physics and superfluid-insulator transition in ultracold Fermi gases. We consider the type of SOC that has been realized in cold atoms experiments via two-photon Raman processes. Our analyses are based on the knowledge of full single-particle spectrum in lattices, without relying on any tightbinding approximation.We evaluate existing tight-binding models and point out their limitations in predicting the correct single-particle physics due to the missed high-band contributions. Moreover, we show that the Raman field (creating SOC) can induce band-gap closing in a two-dimensional optical lattice, leading to the intriguing phenomenon of superfluidity-reentrance for interacting fermions at integer filling. We present the superfluid-insulator phase diagram in a wide parameter regime of chemical potentials and Raman fields. All these results are far beyond any tight-binding model can predict, and can be directly probed in current cold atoms experiments.

Generation and application of two-photon Raman laser for manipulation of internal state of Cs atom

Two-photon Raman process (TPRP) is an important technique in controlling the atomic internal states. It plays an important role in quantum manipulation and quantum information process. A reliable Raman laser for specific atom is the first step to demonstrate TPRP and quantum manipulation of an atom. In this paper, we theoretically analyze the two-photon Raman process regarding to Cesium “clock states” |6S1/2, F=4, mF=0 and |6S1/2, F=3, mF=0, and we obtain the dependences of the corresponding Rabi frequency on one-and two-photon detunings and one-photon Rabi frequencies in a realistic multi-level Cesium atom system. We find that to obtain an atom state flopping efficiency of 0.99 the Raman laser power fluctuation should be controlled to be smaller than 3.2%. We also report our simple experimental Raman laser system for TPRP of Cesium atom based on a fiber waveguide phase modulator. The phase modulator is driven by a 4.6 GHz microwave source and the two first-order sidebands with a frequency difference of 9.19 GHz are filtered out by a Fabry-Pérot cavity with a finesse of 48. After an amplitude-modulator-based intensity stabilization system, a total power of 73 μupW with a fluctuation of 2.2% within 90 min is obtained. By applying this Raman laser to a single Cesium atom trapped in a micrometer size far-off resonant trap (FORT), we obtain Raman spectra between Cesium “clock states” |6S1/2, F=4, mF=0 and |6S1/2, F=3, mF=0. The discrepancy between the two-photon resonance frequency and the defined clock frequency 9.192631770 GHz is due to the differential Stark shifts by FORT beam and Raman beams as well as the inaccuracy of the microwave source. By varying the Raman pulse length we also show the corresponding Rabi flopping with a rate of 153 kHz, which is consistent with the theoretical calculation. The obtained state transfer efficiency of 0.75 is much smaller than theoretical expectation 0.99, which is mainly limited by the state initialization efficiency. The Raman laser system reported in this paper is simple and reliable to realize and it provides a reliable method to manipulate the Cesium internal state. Moreover it could also be easily extended to other system for quantum manipulation of other species of atom.

Ultrafast saturation of resonant optical processes

A generalized formulation is presented for determining the saturation thresholds for optical processes excited by ultrafast pulses based on the pulse area of the excitation pulse. It is demonstrated that the threshold of driving-pulse intensity for absorption and fluorescence saturation in a two-level system is inversely proportional to the square of the duration of the excitation pulse. These results are obtained from both a simplified analytical solution assuming a Gaussian excitation pulse shape and a detailed numerical calculation based on density-matrix equations. The calculation is generalized further to obtain the saturation condition for a two-photon Raman process by defining a two-photon pulse area both analytically and numerically. These results not only provide predictive capabilities for determining thresholds of signal saturation using ultrashort durations with arbitrary pulse shapes and durations but also open up possibilities for predetermining the threshold intensities of various resonant nonlinear processes.

Quantum state manipulation of single-Cesium-atom qubit in a micro-optical trap

Based on single Cesium atoms trapped in a 1064 nm microscopic optical trap we have exhibited a single qubit encoded in the Cesium “clock states”. The single qubit initialization, detection and the fast state rotation with high efficiencies are demonstrated and this state manipulation is crucial for quantum information processing. The ground states Rabi flopping rate of 229.0 ± 0.6 kHz is realized by a two-photon Raman process. A clock states dephasing time of 3.0±0.7 ms is measured, while an irreversible homogeneous dephasing time of 124±17 ms is achieved by using the spin-echo technique. This well-controlled single atom provides an idea quantum qubit and quantum node for quantum information processing.

Ramsey spectroscopy by direct use of resonant light on isotope atoms for single-photon detuning

We demonstrate Ramsey spectroscopy with cold 87Rb atoms via a two-photon Raman process. One laser beam has a cross-over resonant frequency on the 85Rb transition and the other beam has a 6.8 GHz shifted frequency. These two laser beams fulfill the two-photon Raman resonance condition, which involves a single-photon detuning of −2.6 GHz. By implementing these two lasers on cold 87Rb atoms, we demonstrate Ramsey spectroscopy with an interrogation time of the intermediate state by using π/2 Raman pulses. In our laser system, we can change the single-photon detuning to 1.2, 4.2 or −5.6 GHz by changing the 85Rb transition line used as a locking signal and an injected sideband. The laser system that directly uses resonant light on isotope atoms will be described in this paper.

Topological Fulde-Ferrell superfluid in spin-orbit-coupled atomic Fermi gases

We theoretically predict a new topological matter - topological inhomogeneous Fulde-Ferrell superfluid - in one-dimensional atomic Fermi gases with equal Rashba and Dresselhaus spin-orbit coupling near s-wave Feshbach resonances. The realization of such a spin-orbit coupled Fermi system has already been demonstrated recently by using a two-photon Raman process and the extra one-dimensional confinement is easy to achieve using a tight two-dimensional optical lattice. The topological Fulde-Ferrell superfluid phase is characterized by a nonzero center-of-mass momentum and a non-trivial Berry phase. By tuning the Rabi frequency and the detuning of Raman laser beams, we show that such an exotic topological phase occupies a significant part of parameter space and therefore it could be easily observed experimentally, by using, for example, momentum-resolved and spatially resolved radio-frequency spectroscopy.

Inhomogeneous Fulde-Ferrell superfluidity in spin-orbit-coupled atomic Fermi gases

Inhomogeneous superfluidity lies at the heart of many intriguing phenomena in quantum physics. It is believed to play a central role in unconventional organic or heavy-fermion superconductors, chiral quark matter, and neutron star glitches. However, so far even the simplest form of inhomogeneous superfluidity, the Fulde-Ferrell (FF) pairing state with a single center-of-mass momentum, is not conclusively observed due to the intrinsic complexibility of any realistic Fermi systems in nature. Here we theoretically predict that the controlled setting of ultracold fermionic atoms with synthetic spin-orbit coupling induced by a two-photon Raman process, demonstrated recently in cold-atom laboratories, provides a promising route to realize the long-sought FF superfluidity. At experimentally accessible low temperatures, the FF superfluid state dominates the phase diagram, in sharp contrast to the conventional case without spin-orbit coupling. We show that the finite center-of-mass momentum carried by Cooper pairs is directly measurable via momentum-resolved radio-frequency spectroscopy. Our work opens the way to direct observation and characterization of inhomogeneous superfluidity.

Magnetic-field dependence of Raman coupling in alkali-metal atoms

We calculate the magnetic field dependence of Rabi rates for two-photon optical Raman processes in alkali atoms. Due to a decoupling of the nuclear and electronic spins, these rates fall with increasing field. At the typical magnetic fields of alkali atom Feshbach resonances (B\sim 200G-1200G), the Raman rates have the same order of magnitude as their zero field values, suggesting one can combine Raman-induced gauge fields/spin-orbital coupling with strong Feshbach-induced interactions. The exception is $^6$Li, where there is a factor of 7 suppression in the Raman coupling, compared to its already small zero-field value.