Realization of a Floquet-Engineered Moat Band for Ultracold Atoms

We experimentally engineer a moatlike dispersion in a system of weakly interacting bosons. By periodically modulating the amplitude of a checkerboard optical lattice, the two lowest isolated bands are hybridized such that the single particle energy displays a continuum of nearly degenerate minima that lie along a circle in reciprocal space. The moatlike structure is confirmed by observing a zero group velocity at nonzero quasimomentum and we directly observe the effect of the modified dispersion on the trajectory of the center of mass position of the condensate. We measure the lifetime of condensates loaded into different moat bands at different quasimomenta and compare to theoretical predictions based on a linear stability analysis of Bogoliubov excitations. We find that the condensate decay increases rapidly as the quasimomentum is decreased below the radius of the moat minimum, and argue that such dynamical instability is characteristic of moatlike dispersions, including spin-orbit coupled systems. The ground state of strongly interacting bosons in such degenerate energy landscapes is expected to be highly correlated, and our work represents a step toward realizing fractional quantum Hall-like states of bosons in an optical lattice.

Which Way Does Stimulated Emission Go?

Is it possible to form an image using light produced by stimulated emission? Here we study light scatter off an assembly of excited chromophores. Due to the Optical Theorem, stimulated emission is necessarily accompanied by excited state Rayleigh scattering. Both processes can be used to form images, though they have different dependencies on scattering direction, wavelength and chromophore configuration. Our results suggest several new approaches to optical imaging using fluorophore excited states.

Tunable Three-Body Loss in a Nonlinear Rydberg Medium

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential for generating novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wave function and analytical estimates based on Fermi's golden rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

Exotic Photonic Molecules via Lennard-Jones-like Potentials

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a Förster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters ("molecules") of photons. We demonstrate that for a few-body problem, the multibody interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in two dimensions preferentially arrange themselves in a line configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

Competition between Factors Determining Bright versus Dark Atomic States within a Laser Mode

We observe bimodal fluorescence patterns from atoms in a fast atomic beam when the laser excitation occurs in the presence of a magnetic field and the atoms sample only a portion of the laser profile. The behavior is well explained by competition between the local intensity of the laser, which tends to generate a coherent-population-trapping (CPT) dark state in the J = 1 to J' = 0 system, and the strength of an applied magnetic field that can frustrate the CPT process. This work is relevant for understanding and optimizing the detection process for clocks or other coherent systems utilizing these transitions and could be applicable to in situ calibration of the laser-atom interaction, such as the strength of the magnetic field or laser intensity at a specific location.

Coherent optical nanotweezers for ultracold atoms

There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultracold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work allows for subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.

Realization of a stroboscopic optical lattice for cold atoms with subwavelength spacing

Optical lattices are typically created via the ac Stark shift and are limited by diffraction to periodicities ⩾ λ/2, where λ is the wavelength of light used to create them. Lattices with smaller periodicities may be useful for many-body physics with cold atoms and can be generated by stroboscopic application of a phase-shifted lattice with subwavelength features. Here we demonstrate a λ/4-spaced lattice by stroboscopically applying optical Kronig-Penney-like potentials which are generated using spatially dependent dark states. We directly probe the periodicity of the λ/4-spaced lattice by measuring the average probability density of the atoms loaded into the ground band of the lattice. We measure lifetimes of atoms in this lattice and discuss the mechanisms that limit the applicability of this stroboscopic approach.

Quantum Interference between Photons from an Atomic Ensemble and a Remote Atomic Ion

Many remote-entanglement protocols rely on the generation and interference of photons produced by nodes within a quantum network. Quantum networks based on heterogeneous nodes provide a versatile platform by utilizing the complementary strengths of the differing systems. Implementation of such networks is challenging, due to the disparate spectral and temporal characteristics of the photons generated by the different quantum systems. Here, we report on the observation of quantum interference between photons generated from a single ion and an atomic ensemble. The photons are produced on demand by each source located in separate buildings, in a manner suitable for quantum networking. Given these results, we analyze the feasibility of hybrid ion-ensemble remote entanglement generation.

Microcontroller based scanning transfer cavity lock for long-term laser frequency stabilization

We present a compact all-digital implementation of a scanning transfer cavity lock (STCL) for long-term laser frequency stabilization. An interrupt-driven state machine is employed to realize the STCL with the capability to correct for frequency drifts in the slave laser frequency due to measured changes in the lab environmental conditions. We demonstrate an accuracy of 0.9 MHz for master laser and slave laser wavelengths of 556 nm and 798 nm as an example. The slave laser is also demonstrated to dynamically scan over a wide frequency range while retaining its lock, allowing us to accurately interrogate atomic transitions.

Nanoscale Atomic Density Microscopy

Quantum simulations with ultracold atoms typically create atomic wavefunctions with structures at optical length scales, where direct imaging suffers from the diffraction limit. In analogy to advances in optical microscopy for biological applications, we use a non-linear atomic response to surpass the diffraction limit. Exploiting quantum interference, we demonstrate imaging with super-resolution of λ/50 and excellent temporal resolution of 500 ns. We characterize our microscope's performance by measuring the ensemble averaged probability density of atoms within the unit cells of an optical lattice, and observe the dynamics of atoms excited into motion. This approach can be readily applied to image any atomic or molecular system, as long as it hosts a three-level system.

Parametric heating in a 2D periodically-driven bosonic system: Beyond the weakly-interacting regime

We experimentally investigate the effects of parametric instabilities on the short-time heating process of periodically-driven bosons in 2D optical lattices with a continuous transverse (tube) degree of freedom. We analyze three types of periodic drives: (i) linear along the x-lattice direction only, (ii) linear along the lattice diagonal, and (iii) circular in the lattice plane. In all cases, we demonstrate that the BEC decay is dominated by the emergence of unstable Bogoliubov modes, rather than scattering in higher Floquet bands, in agreement with recent theoretical predictions. The observed BEC depletion rates are much higher when shaking both along x and y directions, as opposed to only x or only y. We also report an explosion of the decay rates at large drive amplitudes, and suggest a phenomenological description beyond Bogoliubov theory. In this strongly-coupled regime, circular drives heat faster than diagonal drives, which illustrates the non-trivial dependence of the heating on the choice of drive.

Heisenberg-scaling measurement protocol for analytic functions with quantum sensor networks

We generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean-squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and we conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

Optical Lattice with Torus Topology

We propose an experimental scheme to construct an optical lattice where the atoms are confined to the surface of a torus. This construction can be realized with spatially shaped laser beams which could be realized with recently developed high resolution imaging techniques. We numerically study the feasibility of this proposal by calculating the tunneling strengths for atoms in the torus lattice. To illustrate the nontrivial role of topology in atomic dynamics on the torus, we study the quantized superfluid currents and fractional quantum Hall (FQH) states on such a structure. For FQH states, we numerically investigate the robustness of the topological degeneracy and propose an experimental way to detect such a degeneracy. Our scheme for torus construction can be generalized to surfaces with higher genus for exploration of richer topological physics.

A low-steering piezo-driven mirror

We present a piezo-driven translatable mirror with excellent pointing stability, capable of driving at frequencies up to tens of kilohertz. Our system uses a tripod of piezo actuators with independently controllable drive voltages, where the ratios of the individual drive voltages are tuned to minimize residual tilting. Attached to a standard ∅ = 12.7 mm mirror, the system has a resonance-free mechanical bandwidth up to 51 kHz, with displacements up to 2 μm at 8 kHz. The maximum static steering error is 5.5 μrad/μm displaced, and the dynamic steering error is lower than 0.6 μrad μm^-1. This simple design should be useful for a large set of optical applications where tilt-free displacements are required, and we demonstrate its application in an ensemble of cold atoms trapped in periodically driven optical lattices.

Optimization of photon storage fidelity in ordered atomic arrays

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. However, these equations are semi-phenomenological, as they treat emission of the atoms into other directions other than the mode of interest as being independent. On the other hand, in systems such as dense, ordered atomic arrays, atoms interact with each other strongly and spatial interference of the emitted light might be exploited to suppress emission into unwanted directions, thereby enabling improved error bounds. Here, we develop a general formalism that fully accounts for spatial interference, and which finds the maximum storage efficiency for a single photon with known spatial input mode into a collection of atoms with discrete, known positions. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number N a like ∼ ( log N a ) 2 ∕ N a 2 , and that, remarkably, an array of just 4 × 4 atoms in principle allows for an error of less than 1%, which is comparable to a disordered ensemble with an optical depth of around 600.

Anomalous Broadening in Driven Dissipative Rydberg Systems

We observe interaction-induced broadening of the two-photon 5s-18s transition in ^{87}Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly 2 orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with blackbody induced population in nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms.

Note: Pneumatically actuated and kinematically positioned optical mounts compatible with laser-cooling experiments

We present two complementary designs of pneumatically actuated and kinematically positioned optics mounts: one designed for vertical mounting and translation, the other designed for horizontal mounting and translation. The design and measured stability make these mounts well-suited to experiments with laser-cooled atoms.

Cold-Atom Magnetism

A trapped cloud of cold atoms can be used to simulate magnetism found in condensed matter systems. [Also see Report by Greif et al. ]

Precision measurement of transition matrix elements via light shift cancellation

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

Absolute transition frequencies and quantum interference in a frequency comb based measurement of the (6,7)Li D lines

Optical frequencies of the D lines of (6,7)Li were measured with a relative accuracy of 5 × 10⁻¹¹ using an optical comb synthesizer. Quantum interference in the laser induced fluorescence for the partially resolved D2 lines was found to produce polarization dependent shifts as large as 1 MHz. Our results resolve large discrepancies among previous experiments and between all experiments and theory. The fine-structure splittings for ⁶Li and ⁷Li are 10052.837(22) MHz and 10053.435(21) MHz. The splitting isotope shift is 0.599(30) MHz, in reasonable agreement with recent theoretical calculations.

Pulsed Sisyphus scheme for laser cooling of atomic (anti)hydrogen

We propose a laser cooling technique in which atoms are selectively excited to a dressed metastable state whose light shift and decay rate are spatially correlated for Sisyphus cooling. The case of cooling magnetically trapped (anti)hydrogen with the 1S-2S-3P transitions by using pulsed ultraviolet and continuous-wave visible lasers is numerically simulated. We find a number of appealing features including rapid three-dimensional cooling from ∼1 K to recoil-limited, millikelvin temperatures, as well as suppressed spin-flip loss and manageable photoionization loss.

Differential light-shift cancellation in a magnetic-field-insensitive transition of 87rb

The precise measurement of transition frequencies of trapped atomic samples is susceptible to inaccuracy arising from the inhomogeneous differential shift of the relevant energy levels in the presence of the trapping fields. We demonstrate near-complete cancellation of the differential ac Stark shift ("light shift") of a two-photon magnetic-field-insensitive microwave hyperfine (clock) transition in ^{87}Rb atoms trapped in an optical lattice. Up to 95(2)% of the differential light shift is cancelled while maintaining magnetic-field insensitivity. This technique should have applications in quantum information and frequency metrology.

Economic evaluations of HIV treatment and health research with people diagnosed with HIV infection and co-occurring mental health and substance use disorders

This paper describes the research challenges involved in measuring costs in economic evaluations of patients who are coping simultaneously with HIV/AIDS and co-occurring mental health and substance abuse disorders-especially in multi-site studies. We describe the general issues that arise in measuring costs for this population and suggest some operational solutions for their resolution, drawing from our experience in a recent multi-site health services research study focused on this population. We show that while reliance on patient self-report data may be unavoidable to provide a common denominator in multi-site studies, there are also some practical ways of improving the accuracy of such data and the cost estimates that result from them. We also provide readers with a means for securing the data collection instruments developed for the cost component of this study in the hope that these may serve as templates for researchers doing similar work.

Phases of a two-dimensional bose gas in an optical lattice

Ultracold atoms in optical lattices realize simple condensed matter models. We create an ensemble of ≈60 harmonically trapped 2D Bose-Hubbard systems from a 87Rb Bose-Einstein condensate in an optical lattice and use a magnetic resonance imaging approach to select a few 2D systems for study, thereby eliminating ensemble averaging. Our identification of the transition from superfluid to Mott insulator, as a function of both atom density and lattice depth, is in excellent agreement with a universal state diagram [M. Rigol, Phys. Rev. A 79 053605 (2009)] suitable for our trapped system. In agreement with theory, our data suggest a failure of the local density approximation in the transition region.

Multiphoton magnetooptical trap

We demonstrate a magnetooptical trap (MOT) configuration which employs optical forces due to light scattering between electronically excited states of the atom. With the standard MOT laser beams propagating along the x and y directions, the laser beams along the z direction are at a different wavelength that couples two sets of excited states. We demonstrate efficient cooling and trapping of cesium atoms in a vapor cell and sub-Doppler cooling on both the red and blue sides of the two-photon resonance. The technique demonstrated in this work may have applications in background-free detection of trapped atoms, and in assisting laser cooling and trapping of certain atomic species that require cooling lasers at inconvenient wavelengths.

Bose-Einstein condensate in a uniform light-induced vector potential

We use a two-photon dressing field to create an effective vector gauge potential for Bose-Einstein-condensed 87Rb atoms in the F=1 hyperfine ground state. These Raman-dressed states are spin and momentum superpositions, and we adiabatically load the atoms into the lowest energy dressed state. The effective Hamiltonian of these neutral atoms is like that of charged particles in a uniform magnetic vector potential whose magnitude is set by the strength and detuning of the Raman coupling. The spin and momentum decomposition of the dressed states reveals the strength of the effective vector potential, and our measurements agree quantitatively with a simple single-particle model. While the uniform effective vector potential described here corresponds to zero magnetic field, our technique can be extended to nonuniform vector potentials, giving nonzero effective magnetic fields.

Quantum and classical dynamics of a Bose-Einstein condensate in a large-period optical lattice

We experimentally investigate diffraction of a 87Rb Bose-Einstein condensate from a one-dimensional optical lattice. We use a range of lattice periods and timescales, including those beyond the Raman-Nath limit. We compare the results to numerical solutions of the Gross-Pitaevskii equation and classical calculations, with quantitative and qualitative agreement, respectively. The classical calculations predict that the envelope of the time-evolving diffraction pattern is shaped by caustics: singularities in the phase-space density of classical trajectories. This behavior becomes increasingly clear as the lattice period grows.

Atoms in a radio-frequency-dressed optical lattice

We load cold atoms into an optical lattice dramatically reshaped by radio-frequency coupling of state-dependent lattice potentials. This radio-frequency dressing changes the unit cell of the lattice at a subwavelength scale, such that its curvature and topology departs strongly from that of a simple sinusoidal lattice potential. Radio-frequency dressing has previously been performed at length scales from mm to tens of mum, but not at the single-optical-wavelength scale. At this length scale significant coupling between adiabatic potentials leads to nonadiabatic transitions, which we measure as a function of lattice depth and dressing amplitude. We also investigate the dressing by measuring changes in the momentum distribution of the dressed states.

Condensate fraction in a 2D Bose gas measured across the Mott-insulator transition

We realize a single-band 2D Bose-Hubbard system with Rb atoms in an optical lattice and measure the condensate fraction as a function of lattice depth, crossing from the superfluid to the Mott-insulating phase. We quantitatively identify the location of the superfluid to normal transition by observing when the condensed fraction vanishes. Our measurement agrees with recent quantum Monte Carlo calculations for a finite-sized 2D system to within experimental uncertainty.

Controlled exchange interaction between pairs of neutral atoms in an optical lattice

Ultracold atoms trapped by light offer robust quantum coherence and controllability, providing an attractive system for quantum information processing and for the simulation of complex problems in condensed matter physics. Many quantum information processing schemes require the manipulation and deterministic entanglement of individual qubits; this would typically be accomplished using controlled, state-dependent, coherent interactions among qubits. Recent experiments have made progress towards this goal by demonstrating entanglement among an ensemble of atoms confined in an optical lattice. Until now, however, there has been no demonstration of a key operation: controlled entanglement between atoms in isolated pairs. Here we use an optical lattice of double-well potentials to isolate and manipulate arrays of paired (87)Rb atoms, inducing controlled entangling interactions within each pair. Our experiment realizes proposals to use controlled exchange coupling in a system of neutral atoms. Although 87Rb atoms have nearly state-independent interactions, when we force two atoms into the same physical location, the wavefunction exchange symmetry of these identical bosons leads to state-dependent dynamics. We observe repeated interchange of spin between atoms occupying different vibrational levels, with a coherence time of more than ten milliseconds. This observation demonstrates the essential component of a neutral atom quantum SWAP gate (which interchanges the state of two qubits). Its 'half-implementation', the root SWAP gate, is entangling, and together with single-qubit rotations it forms a set of universal gates for quantum computation.

Sublattice addressing and spin-dependent motion of atoms in a double-well lattice

We load atoms into every site of an optical lattice and selectively spin flip atoms in a sublattice consisting of every other site. These selected atoms are separated from their unselected neighbors by less than an optical wavelength. We also show spin-dependent transport, where atomic wave packets are coherently separated into adjacent sites according to their internal state. These tools should be useful for quantum information processing and quantum simulation of lattice models with neutral atoms.

Preparing and probing atomic number states with an atom interferometer

We describe the controlled loading and measurement of number-squeezed states and Poisson states of atoms in individual sites of a double well optical lattice. These states are input to an atom interferometer that is realized by symmetrically splitting individual lattice sites into double wells, allowing atoms in individual sites to evolve independently. The two paths then interfere, creating a matter-wave double-slit diffraction pattern. The time evolution of the double-slit diffraction pattern is used to measure the number statistics of the input state. The flexibility of our double well lattice provides a means to detect the presence of empty lattice sites, an important and so far unmeasured factor in determining the purity of a Mott state.

Mott-insulator transition in a two-dimensional atomic Bose gas

Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and study the resulting Mott insulator. The measured momentum distributions agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.

Strongly inhibited transport of a degenerate 1D Bose gas in a lattice

We report the observation of strongly damped dipole oscillations of a quantum degenerate 1D atomic Bose gas in a combined harmonic and optical lattice potential. Damping is significant for very shallow axial lattices (0.25 photon recoil energies), and increases dramatically with increasing lattice depth, such that the gas becomes nearly immobile for times an order of magnitude longer than the single-particle tunneling time. Surprisingly, we see no broadening of the atomic quasimomentum distribution after damped motion. Recent theoretical work suggests that quantum fluctuations can strongly damp dipole oscillations of a 1D atomic Bose gas, providing a possible explanation for our observations.

Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas

We investigate the correlation properties of a one-dimensional interacting Bose gas by loading a magnetically trapped 87Rb Bose-Einstein condensate (BEC) into a deep two-dimensional optical lattice. We measure the three-body recombination rate for both the BEC in the magnetic trap and the BEC loaded into the optical lattice. The recombination rate coefficient is a factor of 7 smaller in the lattice, which we interpret as a reduction in the local three-body correlation function in the 1D case. This is a signature of correlation intermediate between that of the uncorrelated, phase coherent, 1D, mean-field regime and the strongly correlated Tonks-Girardeau regime.

Quantum information with neutral atoms as qubits

One of the essential features of a quantum computer is a quantum 'register' of well-characterized qubits. Neutral atoms in optical lattices are a natural candidate for such a register. We have demonstrated a patterned-loading technique that can be used to load atoms into large arrays of tightly confined but optically resolvable lattice sites. We have also seen preliminary indications of the Mott-insulator transition, which provides a route for single-atom initialization of the individual sites. Combining the two experiments should allow for large arrays of individually addressable single atoms, a system which provides a starting point for further quantum computation studies.

Analysis of broadband x-ray spectra of highly charged krypton from a microcalorimeter detector of an electron-beam ion trap

Spectra of highly charged Kr ions, produced in an electron-beam ion trap (EBIT), have been recorded in a broad x-ray energy band (0.3 keV to 4 keV) with a microcalorimeter detector. Most of the spectral lines have been identified as transitions of B- to Al-like Kr. The transition energies have been determined with 0.2% uncertainty. A semi-empirical EBIT plasma model has been created to calculate a synthetic spectrum of highly charged Kr and to determine a charge state distribution of Kr ions inside the EBIT.

Costs and benefits of treatment for cocaine addiction in DATOS

Our objective was to examine the cost of long-term residential (LTR) and outpatient drug-free (ODF) treatments for cocaine-dependent patients participating in the Drug Abuse Treatment Outcome Studies (DATOS), calculate the tangible cost of crime to society, and determine treatment benefits. Subjects were 502 cocaine-dependent patients selected from a national and naturalistic nonexperimental evaluation of community-based treatment. Financial data were available for programs from 10 US cities where the subjects received treatment between 1991 and 1993. Treatment costs were estimated from the 1992 National Drug Abuse Treatment Unit Survey (NDATUS), and tangible costs of crime were estimated from reports of illegal acts committed before, during, and after treatment. Sensitivity analyses examined results for three methods of estimating the costs of crime and cost-benefit ratios. Results showed that cocaine-dependent patients treated in both LTR and ODF programs had reductions in costs of crime from before to after treatment. LTR patients had the highest levels and costs of crime before treatment, had the greatest amount of crime cost reductions in the year after treatment, and yielded the greatest net benefits. Cost-benefit ratios for both treatment modalities provided evidence of significant returns on treatment investments for cocaine addiction.