Search

A method for mitigating the readout delay characteristic of Bragg-based atom interferometry is presented, utilizing an asymmetric Mach-Zehnder interferometer sequence to generate spatial fringes that are read out while still overlapped. The time of flight after the final beamsplitter is engineered to facilitate constructive overlap of the fringes on the output states. A noise analysis performed using a precision atom interferometer is presented, comparing the traditional separated symmetric scheme with that of the separated and overlapped asymmetric scheme showing no significant increase in short term phase noise., Comment: 7 pages, 5 figures

The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective 1D Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matterwave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the purely classical simulation, suggesting that observing such exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the non-interacting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms., Comment: Close to the published version

We present three-dimensional simulations of a protoplanetary disk subject to the effect of a nearby (0.3pc distant) supernova, using a time-dependent flow from a one dimensional numerical model of the supernova remnant (SNR), in addition to constant peak ram pressure simulations. Simulations are performed for a variety of disk masses and inclination angles. We find disk mass-loss rates that are typically 1e-7 to 1e-6 Msol/yr (but peak near 1e-5 Msol/yr during the "instantaneous" stripping phase) and are sustained for around 200 yr. Inclination angle has little effect on the mass loss unless the disk is close to edge-on. Inclined disks also strip asymmetrically with the trailing edge ablating more easily. Since the interaction lasts less than one outer rotation period, there is not enough time for the disk to restore its symmetry, leaving the disk asymmetrical after the flow has passed. Of the low-mass disks considered, only the edge-on disk is able to survive interaction with the SNR (with 50% of its initial mass remaining). At the end of the simulations, disks that survive contain fractional masses of SN material up to 5e-6. This is too low to explain the abundance of short-lived radionuclides in the early solar system, but a larger disk and the inclusion of radiative cooling might allow the disk to capture a higher fraction of SN material., Comment: 16 pages, 16 figures, 2 tables, accepted by MNRAS

We observe the breakup dynamics of an elongated cloud of condensed $^{85}$Rb atoms placed in an optical waveguide. The number of localized spatial components observed in the breakup is compared with the number of solitons predicted by a plane-wave stability analysis of the nonpolynomial nonlinear Schr\"odinger equation, an effective one-dimensional approximation of the Gross-Pitaevskii equation for cigar-shaped condensates. It is shown that the numbers predicted from the fastest growing sidebands are consistent with the experimental data, suggesting that modulational instability is the key underlying physical mechanism driving the breakup., Comment: 6 pages, 5 figures

This paper presents the first realisation of a simultaneous $^{87}$Rb -$^{85}$Rb Mach-Zehnder atom interferometer with Bose-condensed atoms. A number of ambitious proposals for precise terrestrial and space based tests of the Weak Equivalence Principle rely on such a system. This implementation utilises hybrid magnetic-optical trapping to produce spatially overlapped condensates with a duty cycle of 20s. A horizontal optical waveguide with co-linear Bragg beamsplitters and mirrors is used to simultaneously address both isotopes in the interferometer. We observe a non-linear phase shift on a non-interacting $^{85}$Rb interferometer as a function of interferometer time, $T$, which we show arises from inter-isotope scattering with the co-incident $^{87}$Rb interferometer. A discussion of implications for future experiments is given., Comment: 7 pages, 5 figures. The authors welcome comments and feedback on this manuscript

We perform three dimensional hydrodynamic simulations of the ram pressure stripping of the hot extended gaseous halo of a massive galaxy using the k-epsilon sub-grid turbulence model at Mach numbers 0.9, 1.1 and 1.9. The k-epsilon model is used to simulate high Reynolds number flows by increasing the transport coefficients in regions of high turbulence. We find that the initial, instantaneous stripping is the same whether or not the k-epsilon model is implemented and is in agreement with the results of other studies. However the use of the k-epsilon model leads to five times less gas remaining after stripping by a supersonic flow has proceeded for 10 Gyr, which is more consistent with what simple analytic calculations indicate. Hence the continual Kelvin-Helmholtz stripping plays a significant role in the ram pressure stripping of the haloes of massive galaxies. To properly account for this, simulations of galaxy clusters will require the use of sub-grid turbulence models, Comment: 10 pages, 8 figures, 3 tables; accepted for publication in MNRAS

We demonstrate a horizontal, linearly guided Mach Zehnder atom interferometer in an optical waveguide. Intended as a proof-of-principle experiment, the interferometer utilises a Bose-Einstein condensate in the magnetically insensitive |F=1,mF=0> state of Rubidium-87 as an acceleration sensitive test mass. We achieve a modest sensitivity to acceleration of da = 7x10^-4 m/s^2. Our fringe visibility is as high as 38% in this optically guided atom interferometer. We observe a time-of-flight in the waveguide of over half a second, demonstrating the utility of our optical guide for future sensors., Comment: 6 pages, 3 figures. Submitted to Phys. Rev. A

We review experimental progress on atom lasers out-coupled from Bose-Einstein condensates, and consider the properties of such beams in the context of precision inertial sensing. The atom laser is the matter-wave analog of the optical laser. Both devices rely on Bose-enhanced scattering to produce a macroscopically populated trapped mode that is output-coupled to produce an intense beam. In both cases, the beams often display highly desirable properties such as low divergence, high spectral flux and a simple spatial mode that make them useful in practical applications, as well as the potential to perform measurements at or below the quantum projection noise limit. Both devices display similar second-order correlations that differ from thermal sources. Because of these properties, atom lasers are a promising source for application to precision inertial measurements., Comment: This is a review paper. It contains 40 pages, including references and figures

We present a precision gravimeter based on coherent Bragg diffraction of freely falling cold atoms. Traditionally, atomic gravimeters have used stimulated Raman transitions to separate clouds in momentum space by driving transitions between two internal atomic states. Bragg interferometers utilize only a single internal state, and can therefore be less susceptible to environmental perturbations. Here we show that atoms extracted from a magneto-optical trap using an accelerating optical lattice are a suitable source for a Bragg atom interferometer, allowing efficient beamsplitting and subsequent separation of momentum states for detection. Despite the inherently multi-state nature of atom diffraction, we are able to build a Mach-Zehnder interferometer using Bragg scattering which achieves a sensitivity to the gravitational acceleration of $\Delta g/g = 2.7\times10^{-9}$ with an integration time of 1000s. The device can also be converted to a gravity gradiometer by a simple modification of the light pulse sequence., Comment: 13 pages, 11 figures

Massive stars form whilst they are still embedded in dense envelopes. As a result, the roles of rotation, mass loss and accretion in massive star formation are not well understood. This study evaluates the source of the Q-band, lambda=19.5 microns, emission of massive young stellar objects (MYSOs). This allows us to determine the relative importance of rotation and outflow activity in shaping the circumstellar environments of MYSOs on 1000 AU scales. We obtained diffraction limited mid-infrared images of a sample of 20 MYSOs using the VLT/VISIR and Subaru/COMICS instruments. For these 8 m class telescopes and the sample selected, the diffraction limit, ~0.6", corresponds to approximately 1000 AU. We compare the images and the spectral energy distributions (SEDs) observed to a 2D, axis-symmetric dust radiative transfer model that reproduces VLTI/MIDI observations of the MYSO W33A. We vary the inclination, mass infall rate, and outflow opening angle to simultaneously recreate the behaviour of the sample of MYSOs in the spatial and spectral domains. The mid-IR emission of 70 percent of the MYSOs is spatially resolved. In the majority of cases, the spatial extent of their emission and their SEDs can be reproduced by the W33A model featuring an in-falling, rotating dusty envelope with outflow cavities. There is independent evidence that most of the sources which are not fit by the model are associated with ultracompact HII regions and are thus more evolved. We find that, in general, the diverse 20 micron morphology of MYSOs can be attributed to warm dust in the walls of outflow cavities seen at different inclinations. This implies that the warm dust in the outflow cavity walls dominates the Q-band emission of MYSOs. In turn, this emphasises that outflows are an ubiquitous feature of massive star formation., Comment: Accepted for publication in A&A. The images in this version have been compressed. A high resolution version is available on request

We present a narrow linewidth continuous laser source with over 11 Watts of output power at 780nm, based on single-pass frequency doubling of an amplified 1560nm fibre laser with 36% efficiency. This source offers a combination of high power, simplicity, mode quality and stability. Without any active stabilization, the linewidth is measured to be below 10kHz. The fibre seed is tunable over 60GHz, which allows access to the D2 transitions in 87Rb and 85Rb, providing a viable high-power source for laser cooling as well as for large-momentum-transfer beamsplitters in atom interferometry. Sources of this type will pave the way for a new generation of high flux, high duty-cycle degenerate quantum gas experiments., Comment: 5 pages, 3 figures

Collapsing Bose-Einstein condensates are rich and complex quantum systems for which quantitative explanation by simple models has proved elusive. We present new experimental data on the collapse of high density Rb-85 condensates with attractive interactions and find quantitative agreement with the predictions of the Gross-Pitaevskii equation. The collapse data and measurements of the decay of atoms from our condensates allow us to put new limits on the value of the Rb-85 three-body loss coefficient K_3 at small positive and negative scattering lengths., Comment: 6 pages, 5 figures

We present a cold atom gravimeter operating with a sample of Bose-condensed Rubidium-87 atoms. Using a Mach-Zehnder configuration with the two arms separated by a two-photon Bragg transition, we observe interference fringes with a visibility of 83% at T=3 ms. We exploit large momentum transfer (LMT) beam splitting to increase the enclosed space-time area of the interferometer using higher-order Bragg transitions and Bloch oscillations. We also compare fringes from condensed and thermal sources, and observe a reduced visibility of 58% for the thermal source. We suspect the loss in visibility is caused partly by wavefront aberrations, to which the thermal source is more susceptible due to its larger transverse momentum spread. Finally, we discuss briefly the potential advantages of using a coherent atomic source for LMT, and present a simple mean-field model to demonstrate that with currently available experimental parameters, interaction-induced dephasing will not limit the sensitivity of inertial measurements using freely-falling, coherent atomic sources., Comment: 6 pages, 4 figures. Final version, published PRA

We present a Ramsey-type atom interferometer operating with an optically trapped sample of 10^6 Bose-condensed Rb-87 atoms. The optical trap allows us to couple the |F =1, mF =0>\rightarrow |F =2, mF =0> clock states using a single photon 6.8GHz microwave transition, while state selective readout is achieved with absorption imaging. Interference fringes with contrast approaching 100% are observed for short evolution times. We analyse the process of absorption imaging and show that it is possible to observe atom number variance directly, with a signal-to-noise ratio ten times better than the atomic projection noise limit on 10^6 condensate atoms. We discuss the technical and fundamental noise sources that limit our current system, and outline the improvements that can be made. Our results indicate that, with further experimental refinements, it will be possible to produce and measure the output of a sub-shot-noise limited, large atom number BEC-based interferometer. In an addendum to the original paper, we attribute our inability to observe quantum projection noise to the stability of our microwave oscillator and background magnetic field. Numerical simulations of the Gross-Pitaevskii equations for our system show that dephasing due to spatial dynamics driven by interparticle interactions account for much of the observed decay in fringe visibility at long interrogation times. The simulations show good agreement with the experimental data when additional technical decoherence is accounted for, and suggest that the clock states are indeed immiscible. With smaller samples of 5 \times 10^4 atoms, we observe a coherence time of {\tau} = (1.0+0.5-0.3) s., Comment: 22 pages, 6 figures Addendum: 11 pages, 6 figures

We describe our experimental setup for creating stable Bose-Einstein condensates of Rb-85 with tunable interparticle interactions. We use sympathetic cooling with Rb-87 in two stages, initially in a tight Ioffe-Pritchard magnetic trap and subsequently in a weak, large-volume crossed optical dipole trap, using the 155 G Feshbach resonance to manipulate the elastic and inelastic scattering properties of the Rb-85 atoms. Typical Rb-85 condensates contain 4 x 10^4 atoms with a scattering length of a=+200a_0. Our minimalist apparatus is well-suited to experiments on dual-species and spinor Rb condensates, and has several simplifications over the Rb-85 BEC machine at JILA (Papp, 2007; Papp and Wieman, 2006), which we discuss at the end of this article., Comment: 10 pages, 8 figures

Every measurement of the population in an uncorrelated ensemble of two-level systems is limited by what is known as the quantum projection noise limit. Here, we present quantum projection noise limited performance of a Ramsey type interferometer using freely propagating coherent atoms. The experimental setup is based on an electro-optic modulator in an inherently stable Sagnac interferometer, optically coupling the two interfering atomic states via a two-photon Raman transition. Going beyond the quantum projection noise limit requires the use of reduced quantum uncertainty (squeezed) states. The experiment described demonstrates atom interferometry at the fundamental noise level and allows the observation of possible squeezing effects in an atom laser, potentially leading to improved sensitivity in atom interferometers., Comment: 8 pages, 8 figures, published in Phys. Rev. A

We study the properties of an atom laser beam derived from a Bose-Einstein condensate using three different outcouplers, one based on multi-state radio frequency transitions and two others based on Raman transitions capable of imparting momentum to the beam. We first summarize the differences that arise in such systems, and how they may impact on the use of an atom laser in interferometry. Experimentally, we examine the formation of a bound state in all three outcouplers, a phenomenon which limits the atom laser flux, and find that a two-state Raman outcoupler is the preferred option for high flux, low divergence atom laser beams., Comment: 8 Pages, 5 Figures, Submitted to PRA

We observe coherent, continuous wave, 455nm blue beam production via frequency up-conversion in cesium vapor. Two infrared lasers induce strong double-excitation in a heated cesium vapor cell, allowing the atoms to undergo a double cascade and produce a coherent, collimated, blue beam co-propagating with the two infrared pump lasers., Comment: 4 pages, 4 figures

We report on the observation and characterisation of an inelastic loss feature in collisions between ultracold Rb-85 |F=2, m_F=-2> atoms at a magnetic field of 220 G. Our apparatus creates ultracold Rb-85 clouds by sympathetic cooling with a Rb-87 reservoir, and can produce pure Rb-87 condensates of 10^6 atoms by a combination of evaporative cooling in a quadrupole-Ioffe magnetic trap and further evaporation in a weak, large-volume optical dipole trap. By combining Rb-85 and Rb-87 atoms collected in a dual-species magneto-optical trap and selectively evaporating the heavier isotope, we demonstrate strong sympathetic cooling of the Rb-85 cloud, increasing its phase space density by three orders of magnitude with no detectable loss in number. We have used ultracold samples created in this way to observe the variation of inelastic loss in ultracold Rb-85 as a function of magnetic field near the 155 G Feshbach resonance. We have also measured a previously unobserved loss feature at 219.9(1) G with a width of 0.28(6) G, which we associate with a narrow Feshbach resonance predicted by theory., Comment: 4 pages, 3 figures, content changed

In this work, we examine a system for coherent transfer of atoms into a Bose-Einstein condensate. We utilize two spatially separate Bose-Einstein condensates in different hyperfine ground states held in the same dc magnetic trap. By means of a pulsed transfer of atoms, we are able to show a clear resonance in the timing of the transfer, both in temperature and number, from which we draw conclusions about the underlying physical process. The results are discussed in the context of the recently demonstrated pumped atom laser., Comment: 5 pages, 5 figures, published in Physical Review A

We present results on a Raman laser-system that resonantly drives a closed two-photon transition between two levels in different hyperfine ground states of 87Rb. The coupler is based on a novel optical design for producing two phase-coherent optical beams to drive a Raman transition. Operated as an outcoupler, it produces an atom laser in a single internal atomic state, with the lower divergence and increased brightness typical of a Raman outcoupler. Due to the optical nature of the outcoupling, the two-state outcoupler is an ideal candidate for transferring photon correlations onto atom-laser beams. As our laser system couples just two hyperfine ground states, it has also been used as an internal state beamsplitter, taking the next major step towards free space Ramsey interferometry with an atom laser., Comment: 7 Pages, 4 figures: Revised and published in Optics Express

We present results on a free-space atom interferometer operating on the first order magnetically insensitive |F=1,mF=0> -> |F=2,mF=0> transition of Bose-condensed 87Rb atoms. A pulsed atom laser is output-coupled from a Bose-Einstein condensate and propagates through a sequence of two internal state beam splitters, realized via coherent Raman transitions between the two interfering states. We observe Ramsey fringes with a visibility close to 100% and determine the current and the potentially achievable interferometric phase sensitivity. This system is well suited to testing recent proposals for generating and detecting squeezed atomic states., Comment: published version, 8 pages, 3 figures

We present a thorough analysis of single atom detection using optical cavities. The large set of parameters that influence the signal-to-noise ratio for cavity detection is considered, with an emphasis on detunings, probe power, cavity finesse and photon detection schemes. Real device operating restrictions for single photon counting modules and standard photodiodes are included in our discussion, with heterodyne detection emerging as the clearly favourable technique, particularly for detuned detection at high power., Comment: 11 pages, 8 figures, submitted to PRA, minor changes in Secs. I and IVD.2, and revised Fig.2

A pulsed atom laser derived from a Bose-Einstein condensate is used to probe a second target condensate. The target condensate scatters the incident atom laser pulse. From the spatial distribution of scattered atoms, one can infer important properties of the target condensate and its interaction with the probe pulse. As an example, we measure the s-wave scattering length that, in low energy collisions, describes the interaction between the |F=1,m_F=-1> and |F=2,m_F=0> hyperfine ground states in 87Rb., Comment: published version, 8 pages, 3 figures

We present the experimental realization of a pumped atom laser. We demonstrate the pumping through measurements of the source and laser-mode atom numbers, making a rate equation study of the pumping process., Comment: Version 2 contains 18 pages and 4 figures. We have significantly rewritten the introduction, as well as including a discussion of Rayleigh and Raman superradiant scattering and how these relate to continuous pumping of an atom laser. Five new references were added

We analyze the dynamics of quantum statistics in a harmonically trapped Bose-Einstein condensate, whose two-body interaction strength is controlled via a Feshbach resonance. From an initially non-interacting coherent state, the quantum field undergoes Kerr squeezing, which can be qualitatively described with a single mode model. To render the effect experimentally accessible, we propose a homodyne scheme, based on two hyperfine components, which converts the quadrature squeezing into number squeezing. The scheme is numerically demonstrated using a two-component Hartree-Fock-Bogoliubov formalism., Comment: 9 pages, 4 figures

We report the experimental realisation of a multibeam atom laser. A single continuous atom laser is outcoupled from a Bose-Einstein condensate (BEC) via an optical Raman transition. The atom laser is subsequently split into up to five atomic beams with slightly different momenta, resulting in multiple, nearly co-propagating, coherent beams which could be of use in interferometric experiments. The splitting process itself is a novel realization of Bragg diffraction, driven by each of the optical Raman laser beams independently. This presents a significantly simpler implementation of an atomic beam splitter, one of the main elements of coherent atom optics.

We present experimental and theoretical results showing the improved beam quality and reduced divergence of an atom laser produced by an optical Raman transition, compared to one produced by an RF transition. We show that Raman outcoupling can eliminate the diverging lens effect that the condensate has on the outcoupled atoms. This substantially improves the beam quality of the atom laser, and the improvement may be greater than a factor of ten for experiments with tight trapping potentials. We show that Raman outcoupling can produce atom lasers whose quality is only limited by the wavefunction shape of the condensate that produces them, typically a factor of 1.3 above the Heisenberg limit., Comment: Corrected analysis, added figure

We investigate the spatial structure and temporal dynamics created in a Bose-Einstein condensate (BEC) by radio-frequency (RF) atom laser output-couplers using a one-dimensional mean-field model. We compare the behavior of a `pure' two-state atom laser to the multi-level systems demonstrated in laboratories. In particular, we investigate the peak homogeneous output flux, classical fluctuations in the beam and the onset of a bound state which shuts down the atom laser output., Comment: 9 pages, 8 figures

In this paper we present experimental results and theory on the first continuous (long pulse) Raman atom laser. The brightness that can be achieved with this system is three orders of magnitude greater than has been previously demonstrated in any other continuously outcoupled atom laser. In addition, the energy linewidth of a continuous atom laser can be made arbitrarily narrow compared to the mean field energy of a trapped condensate. We analyze the flux and brightness of the atom laser with an analytic model that shows excellent agreement with experiment with no adjustable parameters., Comment: 4 pages, 4 black and white figures, submitted to Physical Review

We present the first detector capable of recording high-bandwidth real time atom number density measurements of a Bose Einstein condensate. Based on a two-color Mach-Zehnder interferometer, our detector has a response time that is six orders of magnitude faster than current detectors based on CCD cameras while still operating at the shot-noise limit. With this minimally destructive system it may be possible to implement feedback to stabilize a Bose-Einstein condensate or an atom laser., Comment: 3 pages, 3 figures, submitted to optics letters

We present experimental results demonstrating that the flux of a continuous atom laser beam cannot be arbitrarily increased by increasing the strength of output-coupling. We find that a state changing output-coupler for a continuous atom laser switches off as the output-coupling strength, parameterized by the Rabi frequency, is increased above a critical value of four times the radial trapping frequency. In addition, we find that the continuous atom laser has large classical fluctuations when the Rabi frequency is greater than the radial trapping frequency, due to the output-coupling populating all accessible Zeeman states. The numerical solution of a one-dimensional 5-state Gross-Pitaevskii model for the atom laser is in good qualitative agreement with the experiment., Comment: 4 pages, 5 figures

We demonstrate that there is a fundamental limit to the sensitivity of phase-based detection of atoms with light for a given maximum level of allowable spontaneous emission. This is a generalisation of previous results for two-level and three-level atoms. The limit is due to an upper bound on the phase shift that can be imparted on a laser beam for a given excited state population. Specifially, we show that no single-pass optical technique using classical light, based on any number of lasers or coherences between any number of levels, can exceed the limit imposed by the two-level atom. This puts significant restrictions on potential non-destructive optical measurement schemes., Comment: 7 pages, 1 figure

By direct comparison between experiment and theory, we show how the classical noise on a multi-state atom laser beam increases with increasing flux. The trade off between classical noise and flux is an important consideration in precision interferometric measurement. We use periodic 10 microsecond radio-frequency pulses to couple atoms out of an F=2 87Rb Bose-Einstein condensate. The resulting atom laser beam has suprising structure which is explained using three dimensional simulations of the five state Gross-Pitaevskii equations., Comment: 4 pages, 3 figures

A generalised method of using feedback to control Bose-Einstein condensates is introduced. The condensates are modelled by the Gross-Pitaevskii equation, so only semiclassical fluctations can be suppressed, and back-action from the measurement is ignored. We show that for any available control, a feedback scheme can be found to reduce the energy while the appropriate moment is still dynamic. We demonstrate these schemes by considering a condensate trapped in a harmonic potential that can be modulated in strength and position. The formalism of our feedback scheme also allows the inclusion of certain types of non-linear controls. If the non-linear interaction between the atoms can be controlled via a Feshbach resonance, we show that the feedback process can operate with a much higher efficiency., Comment: 6 pages, 7 figures

We describe the construction and operation of an external cavity diode laser in which the diode is cooled to -45 C. This technique allows us to pull the wavelength of a nominally 782 nm diode to operate at 766.7 nm, a change of over 15 nm. The important aspects of our design are its ease and low cost as compared to other designs of changing the operating wavelength of laser diodes. We provide background information on thermal design with multiple TECs so the reader can extend this example for use in their own applications., Comment: 9 pages, 10 figures

All optical techniques used to probe the properties of Bose-Einstein condensates have been based on dispersion and absorption that can be described by a two-level atom. Both phenomena lead to spontaneous emission that is destructive. Recently, both were shown to lead to the same limit to the signal to noise ratio for a given destruction. We generalise this result to show that no single-pass optical technique using classical light, based on any number of lasers or coherences between any number of levels, can exceed the limit imposed by the two-level atom. This puts significant restrictions on potential non-destructive measurement schemes., Comment: 4 pages, 1 figure

We propose and analyze a series of non-destructive, dynamic detectors for Bose-Einstein condensates based on photo-detectors operating at the shot noise limit. These detectors are compatible with real time feedback to the condensate. The signal to noise ratio of different detection schemes are compared subject to the constraint of minimal heating due to photon absorption and spontaneous emission. This constraint leads to different optimal operating points for interference-based schemes. We find the somewhat counter-intuitive result that without the presence of a cavity, interferometry causes as much destruction as absorption for optically thin clouds. For optically thick clouds, cavity-free interferometry is superior to absorption, but it still cannot be made arbitrarily non-destructive . We propose a cavity-based measurement of atomic density which can in principle be made arbitrarily non-destructive for a given signal to noise ratio.