In order to confine any object, it is necessary to exchange kinetic for potential energy in the trapping field, and in neutral atom traps, the potential energy must be stored as internal atomic energy. Thus practical traps for ground-state neutral atoms are necessarily very shallow compared with thermal energy because the energy level shifts that result from conveniently sized fields are typically considerably smaller than k B T , even for T = 1 K. Neutral atom trapping therefore depends on substantial cooling of a thermal atomic sample, and is often connected with the cooling process. In most practical cases, atoms are loaded from magneto-optical traps, where they have been efficiently accumulated and cooled to mK temperatures (see Sec. 20.3), or from optical molasses, where they have been optically cooled to μK temperatures (see Sec. 19.4). The small depth of typical neutral atom traps dictates stringent vacuum requirements, because an atom cannot remain trapped after a collision with a thermal energy background gas molecule. Since these atoms are vulnerable targets for thermal energy background gas, the mean free time between collisions must exceed the desired trapping time. The cross-section for destructive collisions is quite large because even a gentle collision (i.e. large impact parameter) can impart enough energy to eject an atom from a trap. At pressure P sufficiently low to be of practical interest, the trapping time is ~(10 -8 / P ) s, where P is in torr. This chapter begins with a discussion of ordinary, single-center traps, but also considers arrays of traps. Such “optical lattices” are playing an increasingly important role in research in atomic physics, so discussion of their properties is an appropriate part of the education of a student of the subject. Dipole force optical traps Single-beam optical traps for two-level atoms The simplest imaginable optical trap consists of a single, strongly focused Gaussian laser beam (see Fig. 20.1) [214, 215] whose intensity at the focus varies transversely with r as where is the beam waist size. Such a trap has a well-studied and important macroscopic classical analog in a phenomenon called optical tweezers (see App. 1.C) [216–218].
In order to confine any object, it is necessary to exchange kinetic for potential energy in the trapping field, and in neutral atom traps, the potential energy must be stored as internal atomic energy. Thus practical traps for ground-state neutral atoms are necessarily very shallow compared with thermal energy because the energy level shifts that result from conveniently sized fields are typically considerably smaller than k B T , even for T = 1 K. Neutral atom trapping therefore depends on substantial cooling of a thermal atomic sample, and is often connected with the cooling process. In most practical cases, atoms are loaded from magneto-optical traps, where they have been efficiently accumulated and cooled to mK temperatures (see Sec. 20.3), or from optical molasses, where they have been optically cooled to μK temperatures (see Sec. 19.4). The small depth of typical neutral atom traps dictates stringent vacuum requirements, because an atom cannot remain trapped after a collision with a thermal energy background gas molecule. Since these atoms are vulnerable targets for thermal energy background gas, the mean free time between collisions must exceed the desired trapping time. The cross-section for destructive collisions is quite large because even a gentle collision (i.e. large impact parameter) can impart enough energy to eject an atom from a trap. At pressure P sufficiently low to be of practical interest, the trapping time is ~(10 -8 / P ) s, where P is in torr. This chapter begins with a discussion of ordinary, single-center traps, but also considers arrays of traps. Such “optical lattices” are playing an increasingly important role in research in atomic physics, so discussion of their properties is an appropriate part of the education of a student of the subject. Dipole force optical traps Single-beam optical traps for two-level atoms The simplest imaginable optical trap consists of a single, strongly focused Gaussian laser beam (see Fig. 20.1) [214, 215] whose intensity at the focus varies transversely with r as where is the beam waist size. Such a trap has a well-studied and important macroscopic classical analog in a phenomenon called optical tweezers (see App. 1.C) [216–218].
Microscopically controlled neutral atoms in optical tweezers and lattices have led to exciting advances in the study of quantum information and quantum many-body systems. The light shifts of atomic levels from the trapping potential in these systems can result in detrimental effects such as fluctuating dipole force heating, inhomogeneous detunings, and inhibition of laser cooling, which limits the atomic species that can be manipulated. In particular, these light shifts can be large enough to prevent loading into optical tweezers directly from a magneto-optical trap. We implement a general solution to these limitations by loading, as well as cooling and imaging the atoms with temporally alternating beams, and present an analysis of the role of heating and required cooling for single atom tweezer loading. Because this technique does not depend on any specific spectral properties, it should enable the optical tweezer platform to be extended to nearly any atomic or molecular species that can be laser cooled and optically trapped.
Single atoms are a promising candidate for the creation of a scalable quantum computer. Neutral atoms trapped by optical fields are especially encouraging due to the full controllability of the trap potential. Single neutral atoms trapped within a fibre-fibre cavity allow us to strongly couple atoms and photons. This creates an efficient atom-photon interface which can compensate for the short state transfer distance inherent of neutral atoms. A spatial light modulator allows for the creation and manipulation of an array of these single atom traps.\n\nIn this research we create a setup to cool and trap neutral rubidium-87 atoms by a combination of a magneto-optical trap (MOT) and a dipole trap. The dipole trap uses a strongly focused, far red-detuned laser, which enables us to trap single atoms via the collisional blockade regime. These traps are realised within a novel glass cell, allowing for great optical access.\n\nThe MOT in this setup is able to trap (4.27 +/- 0.10) * 10^3 atoms with a density of (7.89 +/- 0.56) * 10^9 atoms cm^-3 . The MOT temperature is in the order of 100 μK. We also show the manipulation of these properties, allowing us to tailor the MOT. The dipole trap is created with a trap waist of 37 μm, allowing us to trap a cloud of atoms. With the dipole trap we achieve a lifetime of atoms of (34.8 +/- 2.0) ms.
Slowing, cooling, and trapping molecules One of the major achievements in physics during the last two decades of the twentieth century was the ability to cool and trap atoms [1]. Laser cooling can produce previously inconceivable atomic temperatures of less than 1 μK. Atoms with sufficiently low kinetic energy can be trapped in magnetic and optical traps and thus studied for a prolonged time, thereby improving the resolution of spectroscopy by many orders of magnitude as well as reducing Doppler broadening. Furthermore, besides the external degrees of freedom, the internal degrees of freedom of the atoms can also be manipulated, leading to full control of the atoms. One of the holy grails of physics, the achievement of Bose–Einstein condensation in a dilute gas, was achieved mainly because of laser cooling and trapping of atoms. One of the natural extensions of laser cooling and trapping of atoms is the application of the techniques to molecules. Molecules offer a much richer internal structure than atoms, and thus provide extended possibilities to experimentalists. However, atomic laser cooling is based on the repetitive scattering of light and requires a closed, or at least nearly closed, two-level system. Because of the complicated internal structure of molecules, a closed two-level system cannot usually be found because they have many different electronic, vibrational, and rotational states and in general can decay to many different states after absorption of light (see Chap. 16). This requires a complete rethinking of the schemes that are used to cool atoms. Still, because of the extended possibilities cold molecules can offer with respect to cold atoms, there have been a large number of techniques developed to slow, cool, and trap them. These techniques can be divided into two classes, namely direct and indirect cooling. In the first case, molecules at cryogenic or room temperature are directly slowed and cooled. Although many different slowing techniques are used, this chapter focuses on Stark slowing of molecules since it was the first technique developed. Apart from the Stark shift of the molecules, the Zeeman and light shift of molecules can also be used to slow them. The idea behind Stark slowing is to subject the moving molecules to a continuously increasing electric field so that their kinetic energy is converted into potential energy.
The usual form of electromagnetic forces is given by but for neutral atoms q = 0. The next order of force is the dipole term, but this also vanishes because neutral atoms have no inherent dipole moment. However, a dipole moment can be induced by a field, and this is most efficient if the field is alternating near the atomic resonance frequency. Since these frequencies are typically in the optical range, dipole moments are efficiently induced by shining nearly resonant light on the atoms. Laser cooling and trapping rely on the interaction between laser light and atoms to exert a controllable force on the atoms, and many sophisticated schemes have been developed using the special properties of the interaction. This chapter begins with the simplest schemes for exerting optical forces on atoms, namely a single-frequency light field interacting with a two-level atom. Although this is the simplest possible scheme, it is pedagogically valuable because it shows many of the features that will be encountered further on. The ultimate temperature using such a scheme is limited, but lower temperatures can be achieved with multilevel atoms. This topic is addressed later in the chapter. Two kinds of optical forces When an atom absorbs nearly resonant light, it makes a transition to the excited state, and its subsequent return to the ground state can be either by spontaneous or by stimulated emission. The nature of the optical force that arises from these two different processes is quite different, and will be described separately [1]. The spontaneous emission case is different from the familiar quantum mechanical calculations using state vectors to describe the state of the system, because spontaneous emission causes the state of the system to evolve from a pure state into a mixed state (see Exercise 6.9). Spontaneous emission is an essential ingredient for the dissipative nature of the optical forces in monochromatic light, and the density matrix is needed to describe it (see Chap. 6). When an atom absorbs light, its energy excites the atom and its angular momentum changes the electron's orbit. Both of these are internal atomic properties. However, the linear momentum of the light, can change only the external, translational motion of the atom.
In 1925, Einstein predicted the condensation of bosons into the ground state of the system for low (but finite) temperatures. Several phenomena, including superfluidity and superconductivity have been associated with Bose-Einstein condensation, but these systems interact strongly with their environment and pure Bose-Einstein condensation could not be established. It took 70 years, in which time the laser was discovered, and laser cooling techniques to manipulate atoms in a dilute atomic gas, before Bose-Einstein condensation in dilute atomic gases could be demonstrated in 1995. In the first condensation experiments, BECs were created in a magnetic trap. Since in a magnetic trap not all mF states of the atom can be trapped simultaneously, thereby limiting the number of experiments that can be done, other ways of trapping and generating BECs were sought and found. In 2001, the first all-optical BEC was made, where the dipole force was used to trap atoms in the crossing of two far red detuned laser beams. In an optical dipole trap not only atoms in different internal states can be trapped, but also different atomic species simultaneously. In this thesis, the formation of an all-optical Bose-Einstein condensate with rubidium atoms is presented. Conventional all-optical BECs are usually created in high power CO2 laser dipole traps, or have complicated laser cooling schemes and complex dipole trap setups. In our simple and straightforward setup, we load rubidium atoms from a magneto-optical trap into a crossed optical dipole trap created by a single frequency Yb:YAG laser with a wavelength at 1030 nm. The small wavelength allows for a small diffraction limit, and permits us to use standard optical materials, thus making the experimental setup cost effective. Other attempts to achieve Bose-Einstein condensation in a multi-mode (frequency) fiber laser at 1064 nm failed, because the atom loss was quite high. It is assumed that the multi-mode character of the fiber laser induces Raman transitions in rubidium atoms, thereby heating them. We can trap about ∼ 5E7 atoms in a single beam dipole trap out of ∼ 5E9 atoms trapped in theMOT, and ∼ 350,000 atoms can be trapped in a crossed beam dipole trap due to the smaller trap volume. 70% of the atoms in the dipole trap is optically pumped into one mF state. Quantum degeneracy is reached by evaporatively cooling the atoms in the crossed dipole trap by ramping down the laser power with three linear ramps. We can independently change the power of each beam by an AOM. This allows us to use one beam as an atom waveguide for future experiments. After evaporation, we typically have about 10,000 atoms at a temperature below the critical temperature. We have proved Bose-Einstein condensation by using the anisotropic expansion of a quantum degenerate gas trapped in an anisotropic potential. The aspect ratio of our atom cloud changed during a time of flight from 0.7 to 1.2 in 10 ms, thus proving that we have reached quantum degeneracy. We have about 5,000 condensed atoms in our optical dipole trap at a temperature less than 100 nK. The remaining atoms are thermal. Bose-Einstein condensation is obtained within 8 s, and we can repeat the experiment every 30 s. It should be mentioned that the Bose-Einstein experiment was moved from the ”Leibniz Universität Hannover” to the ”Technische Universität Darmstadt”, and had to be completely rebuilt. All-optical Bose-Einstein condensation was reached within one year after the move. Our Bose-Einstein condensation setup presents an ideal starting point for using our condensates in combination with miniaturized atom optical setups based on our novel microfabricated optical elements. With our microlenses, we can create a number of possible dipole trap configurations, such as the dipole trap array or the cylindrical microlens array. Using microlenses in miniaturized atom optical setups opens a completely new field of coherent atom optics. Also because the tight confinement of the microtraps allows us to load a 3D BEC, a 1D BEC, or a Tonks-Girardeau gas in the micropotentials depending on the density.
Our choice of rubidium atoms as the optically active species becomes now clear. The large elasticity of collisions between the electronically excited states of the rubidium D-lines and noble gas atoms has long been proven [25]. The quasi-molecular potential has a depth of the order of kBT, allowing for a significant part of the atoms’ kinetic energy to be extracted. Finally, the cooling transitions are in the near-infrared spectral regime, making them conveniently optically accessible to commercial laser systems. The cooling power Pcool from these experiments can be estimated in a similar way as for anti-Stokes cooling [26, 27] from the mean fluorescence frequency νfl, the incident power Popt, and the absorption probability of the gas mixture at incident frequency ν, α(ν).P Pcool opt fl= -a n n nn( ) (1.1) The typical energy that can be extracted from the sample per cooling cycle is of order of the thermal energy kBT. In the experiments performed so far, we observe cooling powers Pcool in the order of up to 100 mW [17, 23, 28, 29]. Note that it is important to choose a detuning with a high-enough absorption probability a(ν). We are aware that the collisional broadening plays a crucial role here. A measurement of typical fluorescence data recorded with the dense gas mixture will be shown in Section 1.4.1. Experimentally, it turns out to be crucial that the used buffer gas is of high purity to suppress the influence of concurring heating effects, of which quenching is the most known. In the case of quenching, the excitation energy is transferred to an atom of a third species polluting the dense gas mixture when colliding with the quasi-molecule. Relaxation can then occur via nonradiative decay, and so energy is kept in the system, heating the gas. To reduce possible quenching, an effect known to occur, for example, from an admixture with nitrogen, we use a buffer gas with high purity, namely argon gas preferably with a purity of 99.9999 (argon 6.0). Residual heating can also be caused by energy pooling. In this scenario, during the collision of two excited alkali atoms one of them gets further excited. Its relaxation to the ground state implicates the emission of a fluorescence photon with higher energy. For the case of rubidium atoms, the reaction equation of that process can be written as [30]: Rb Rb Rb Rb* * **+ + + Æ + + +mv mv mv mv12 22 12 22 2 2 2 2 . (1.2) The sum of the energies of the single excited rubidium atoms before the collision is higher than the energy of the twice excited atom. The surplus of the energy is thus kept in the system as kinetic energy of the collisional partners [31]. For rubidium atoms subject to a high-pressure noble gas, fluorescence originating from the 6p Æ 5s transition then occurs, and can be detected as blue light at a wavelength λ ≈ 420 nm in the experiments. At room temperature, the alkali atoms are in the solid phase. To produce a sufficient alkali vapor number density the system is heated to temperatures of up to 680 K, while the buffer gas pressure ranges between 50 bar and 230 bar. Under these conditions, we calculate that the dense gas ensemble consists of approximately 1017 cm-3 alkali atoms and 1021 cm-3 noble gas atoms. Then, we can estimate the mean free path length λfp for a gas of colliding atoms (cross section σ) and number density n l sfp = n (1.3) Let us consider the geometric cross section πd2, where d denotes the diameter of a rare gas atom, which is twice the van der Waals radius (d = 2rvdW = 3.76 × 10−10 m for argon [32]). Then, for argon pressure of 200 bar, the mean free path length is in the order of only a few nanometers, λfp ≈ 2.3 nm. Following the Boltzmann distribution, still considering a temperature T = 680 K, one can also estimate the collisional rate to 2.4 × 1011/s. Comparing this to the natural lifetime of the first excited alkali atom level (27 ns), we calculate that 104collisions occur within this period of time. 1.3 Experimental Setup and MethodsIn the following section, we present our experimental setup in detail, including the techniques used to measure atomic fluorescence and temperature changes inside the gas mixture. We offer insights into the high-pressure cells employed (Section 1.3.1), as well as into the spectroscopic techniques (Section 1.3.2) and the thermal deflection setup (Section 1.3.3).