## Thursday, November 25, 2010

### A time-symmetric formulation of quantum mechanics

Quantum mechanics allows one to independently select both the initial and final states of a single system. Such pre- and postselection reveals novel effects that challenge our ideas about what time is and how it flows.

## Thursday, November 18, 2010

### Generation of three-qubit entangled states using superconducting phase qubits

Entanglement is one of the key resources required for quantum computation

^{1}, so the experimental creation and measurement of entangled states is of crucial importance for various physical implementations of quantum computers

^{2}. In superconducting devices

^{3}, two-qubit entangled states have been demonstrated and used to show violations of Bell’s inequality

^{4}and to implement simple quantum algorithms

^{5}. Unlike the two-qubit case, where all maximally entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways

^{6}. These are typified by the states |GHZ = (|000 + |111)/ and |W = (|001 + |010 + |100)/ . Here we demonstrate the operation of three coupled superconducting phase qubits

^{7}and use them to create and measure |GHZ and |W states. The states are fully characterized using quantum state tomography

^{8}and are shown to satisfy entanglement witnesses

^{9}, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.

## Friday, September 24, 2010

### Dynamics of a tunable superfluid junction

We study the population dynamics of a Bose-Einstein condensate in a double-well potential with tunable barrier height. In the regime of weak inter-well coupling, we observe Josephson plasma oscillations as expected. However, in the strong-coupling regime, a second frequency enters the dynamics. We explain the amplitude, frequency, and nature of these two modes by with Gross-Pitaevskii calculations throughout the weak- to strong-coupling crossover. Our results interpolate between two standard paradigms of superfluidity: hydrodynamics and Josephson dynamics.

**Groupmeeting by Lindsay LeBlanc, September 22nd, 2010**

### Simple approach to the relation between laser frequency noise and laser line shape

Frequency fluctuations of lasers cause a broadening of their line shapes. Although the relation between the frequency noise spectrum and the laser line shape has been studied extensively, no simple expression exists to evaluate the laser linewidth for frequency noise spectra that does not follow a power law. We present a simple approach to this relation with an approximate formula for evaluation of the laser linewidth that can be applied to arbitrary noise spectral densities.

### Thermometry with spin-dependent lattices

We propose a method for measuring the temperature of strongly correlated phases of ultracold atom gases confined in spin-dependent optical lattices. In this technique, a small number of 'impurity' atoms—trapped in a state that does not experience the lattice potential—are in thermal contact with atoms bound to the lattice. The impurity serves as a thermometer for the system because its temperature can be straightforwardly measured using time-of-flight expansion velocity. This technique may be useful for resolving many open questions regarding thermalization in these isolated systems. We discuss the theory behind this method and demonstrate proof-of-principle experiments, including the first realization of a three-dimensional (3D) spin-dependent lattice in the strongly correlated regime.

## Wednesday, September 1, 2010

### Photons: Still Bosons

Using Bose-Einstein-statistics-forbidden two-photon excitation in atomic barium, we have limited the rate of statistics-violating transitions, as a fraction $\nu$ of an equivalent statistics-allowed transition rate, to $\nu<4.0\times10^{-11}$ at the 90% confidence level. This is an improvement of more than three orders of magnitude over the best previous result. Additionally, hyperfine-interaction enabling of the forbidden transition has been observed, to our knowledge, for the first time.

## Friday, August 27, 2010

### ECDL with frequency modulation saturation spectroscopy laser lock

## Thursday, August 12, 2010

### An entangled-light-emitting diode

An optical quantum computer, powerful enough to solve problems so far intractable using conventional digital logic, requires a large number of entangled photons

^{1, 2}. At present, entangled-light sources are optically driven with lasers

^{3, 4, 5, 6, 7}, which are impractical for quantum computing owing to the bulk and complexity of the optics required for large-scale applications. Parametric down-conversion is the most widely used source of entangled light, and has been used to implement non-destructive quantum logic gates

^{8, 9}. However, these sources are Poissonian

^{4, 5}and probabilistically emit zero or multiple entangled photon pairs in most cycles, fundamentally limiting the success probability of quantum computational operations. These complications can be overcome by using an electrically driven on-demand source of entangled photon pairs

^{10}, but so far such a source has not been produced. Here we report the realization of an electrically driven source of entangled photon pairs, consisting of a quantum dot embedded in a semiconductor light-emitting diode (LED) structure. We show that the device emits entangled photon pairs under d.c. and a.c. injection, the latter achieving an entanglement fidelity of up to 0.82. Entangled light with such high fidelity is sufficient for application in quantum relays

^{11}, in core components of quantum computing such as teleportation

^{12, 13, 14}, and in entanglement swapping

^{15, 16}. The a.c. operation of the entangled-light-emitting diode (ELED) indicates its potential function as an on-demand source without the need for a complicated laser driving system; consequently, the ELED is at present the best source on which to base future scalable quantum information applications

^{17}.

## Monday, August 9, 2010

### Thermalization of photons

Bose–Einstein condensation1, the macroscopic accumulation of bosonic particles in the energetic ground state below a critical temperature, has been demonstrated in several physical systems2, 3, 4, 5, 6, 7, 8. The perhaps best known example of a bosonic gas, blackbody radiation9, however exhibits no Bose–Einstein condensation at low temperatures10. Instead of collectively occupying the lowest energy mode, the photons disappear in the cavity walls when the temperature is lowered—corresponding to a vanishing chemical potential. Here we report on evidence for a thermalized two-dimensional photon gas with a freely adjustable chemical potential. Our experiment is based on a dye-filled optical microresonator, acting as a ‘white wall’ box for photons. Thermalization is achieved in a photon-number-conserving way by photon scattering off the dye molecules, and the cavity mirrors provide both an effective photon mass and a confining potential—key prerequisites for the Bose–Einstein condensation of photons. As a striking example of the unusual system properties, we demonstrate a yet unobserved light concentration effect into the centre of the confining potential, an effect with prospects for increasing the efficiency of diffuse solar light collection11.

### Deterministic entanglement of two neutral atoms via Rydberg blockade

We demonstrate the first deterministic entanglement of two individually addressed neutral atoms using a Rydberg blockade mediated controlled-NOT gate. Parity oscillation measurements reveal an entanglement fidelity of $F=0.58\pm0.04$, which is above the entanglement threshold of $F=0.5$, without any correction for atom loss, and $F=0.71\pm0.05$ after correcting for background collisional losses. The fidelity results are shown to be in good agreement with a detailed error model.

## Tuesday, July 27, 2010

### Selective and Efficient Process Tomography

We present in a unified manner the existing methods for scalable partial quantum process tomography. We focus on two main approaches: the one presented in Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)], and the ones described, respectively, in Emerson et al. [Science 317, 1893 (2007)] and L\'{o}pez et al. [Phys. Rev. A 79, 042328 (2009)], which can be combined together. The methods share an essential feature: They are based on the idea that the tomography of a quantum map can be efficiently performed by studying certain properties of a twirling of such a map. From this perspective, in this paper we present extensions, improvements and comparative analyses of the scalable methods for partial quantum process tomography. We also clarify the significance of the extracted information, and we introduce interesting and useful properties of the $\chi$-matrix representation of quantum maps that can be used to establish a clearer path toward achieving full tomography of quantum processes in a scalable way.

## Sunday, July 18, 2010

### Noise-Powered Probabilistic Concentration of Phase Information

Phase insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state [1 - 5]. However, this fundamental noise penalty in amplification can be circumvented by resorting to a probabilistic scheme as recently proposed and demonstrated in refs [6 - 8]. These amplifiers are based on highly non-classical resources in a complex interferometer. Here we demonstrate a probabilistic quantum amplifier beating the fundamental quantum limit utilizing a thermal noise source and a photon number subtraction scheme [9]. The experiment shows, surprisingly, that the addition of incoherent noise leads to a noiselessly amplified output state with a phase uncertainty below the uncertainty of the state prior to amplification. This amplifier might become a valuable quantum tool in future quantum metrological schemes and quantum communication protocols.

## Wednesday, July 7, 2010

### Adding control to arbitrary quantum operations

Quantum computers promise exponential power for particular tasks, however, the complexity of quantum algorithms remains a major technological challenge. We have developed and demonstrated an architecture independent technique for adding control qubits to arbitrary quantum operations (unitary or otherwise) - a key requirement in many quantum algorithms. The technique is independent of how the operation is done and does not even require knowledge of what the operation is. In this way the technical problems of how to implement a quantum operation and how to add a control are separated. The number of computational resources required is independent of the depth of the operation and increases only linearly with the number of qubits on which it acts. Our approach will significantly reduce the complexity of quantum computations such as Shor's factoring algorithm and the near-term prospect of quantum simulations. We use this new approach to implement a number of two-qubit photonic quantum gates in which the operation of the control circuit is completed independent of the choice of quantum operation.

### Probing general relativity using atom interferometry

Albert Einstein’s insight that it is impossible to distinguish

^{ }a local experiment in a "freely falling elevator" from one in

^{ }free space led to the development of the theory of general relativity.

^{ }The wave nature of matter manifests itself in a striking way

^{ }in Bose-Einstein condensates, where millions of atoms lose their

^{ }identity and can be described by a single macroscopic wave function.

^{ }We combine these two topics and report the preparation and observation

^{ }of a Bose-Einstein condensate during free fall in a 146-meter-tall

^{ }evacuated drop tower. During the expansion over 1 second, the

^{ }atoms form a giant coherent matter wave that is delocalized

^{ }on a millimeter scale, which represents a promising source for

^{ }matter-wave interferometry to test the universality of free

^{ }fall with quantum matter.

## Wednesday, June 23, 2010

### Towards high-speed optical quantum memories

Quantum memories, capable of controllably storing and releasing a photon, are a crucial component for quantum computers

^{1}and quantum communications

^{2}. To date, quantum memories

^{3, }

^{4, }

^{5, }

^{6}have operated with bandwidths that limit data rates to megahertz. Here we report the coherent storage and retrieval of sub-nanosecond low-intensity light pulses with spectral bandwidths exceeding 1 GHz in caesium vapour. The novel memory interaction takes place through a far off-resonant two-photon transition in which the memory bandwidth is dynamically generated by a strong control field

^{7, }

^{8}. This should allow data rates more than 100 times greater than those of existing quantum memories. The memory works with a total efficiency of 15%, and its coherence is demonstrated through direct interference of the stored and retrieved pulses. Coherence times in hot atomic vapours are on the order of microseconds

^{9}, the expected storage time limit for this memory.

### Ground State Laser Cooling with Electromagnetically Induced Transparency

Ground state laser cooling of a single trapped Ca+ ion is achieved with a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency. Using the Zeeman structure of the S1/2 to P1/2 dipole transition we achieve up to 90% ground state probability. The new method is robust, easy to implement, and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions.

### Suppression of Density Fluctuations in a Quantum Degenerate Fermi Gas

We study density profiles of an ideal Fermi gas and observe Pauli suppression of density fluctuations (atom shot noise) for cold clouds deep in the quantum degenerate regime. Strong suppression is observed for probe volumes containing more than 10,000 atoms. Measuring the level of suppression provides sensitive thermometry at low temperatures. After this method of sensitive noise measurements has been validated with an ideal Fermi gas, it can now be applied to characterize phase transitions in strongly correlated many-body systems.

**Groupmeeting by Dylan Jervis, June 2nd, 2010**

## Thursday, May 13, 2010

## Wednesday, April 28, 2010

### Quantum Theory from 5 reasonable Axioms

The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be derived from five very reasonable axioms. The first four of these are obviously consistent with both quantum theory and classical probability theory. Axiom 5 (which requires that there exists continuous reversible transformations between pure states) rules out classical probability theory. If Axiom 5 (or even just the word "continuous" from Axiom 5) is dropped then we obtain classical probability theory instead. This work provides some insight into the reasons quantum theory is the way it is. For example, it explains the need for complex numbers and where the trace formula comes from. We also gain insight into the relationship between quantum theory and classical probability theory.

### Collective spin squeezing with a cavity

We generate entangled states of an ensemble of 5*10^4 rubidium-87 atoms by optical quantum nondemolition measurement. The resonator-enhanced measurement leaves the atomic ensemble, prepared in a superposition of hyperfine clock levels, in a squeezed spin state. By comparing the resulting reduction of quantum projection noise (up to 8.8(8) dB) with the concomitant reduction of coherence, we demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit.

## Monday, April 19, 2010

### Delocalization of a disordered bosonic system by repulsive interactions

In bosonic many-body systems, disorder tends to localize particles, whereas weak

repulsive interactions between the particles have a delocalizing effect. The crossover

between these regimes has now been studied experimentally, using an optical lattice to

control disorder and interactions independently.

### Non-dispersive optics using storage of light

We demonstrate the non-dispersive deflection of an optical beam in a Stern-Gerlach magnetic field. An optical pulse is initially stored as a spin-wave coherence in thermal rubidium vapour. An inhomogeneous magnetic field imprints a phase gradient onto the spin wave, which upon reacceleration of the optical pulse leads to an angular deflection of the retrieved beam. We show that the obtained beam deflection is non-dispersive, i.e. its magnitude is independent of the incident optical frequency. Compared to a Stern-Gerlach experiment carried out with propagating light under the conditions of electromagnetically induced transparency, the estimated suppression of the chromatic aberration reaches 10 orders of magnitude.

## Thursday, March 18, 2010

### Quantum non-demolition measurements of a qubit coupled to a harmonic oscillator

We theoretically describe the weak measurement of a two-level system (qubit) and quantify the degree to which such a qubit measurement has a quantum non-demolition (QND) character. The qubit is coupled to a harmonic oscillator which undergoes a projective measurement. Information on the qubit state is extracted from the oscillator measurement outcomes, and the QND character of the measurement is inferred by the result of subsequent measurements of the oscillator. We use the positive operator valued measure (POVM) formalism to describe the qubit measurement. Two mechanisms lead to deviations from a perfect QND measurement: (i) the quantum fluctuations of the oscillator, and (ii) quantum tunneling between the qubit states $|0>$ and $|1>$ during measurements. Our theory can be applied to QND measurements performed on superconducting qubits coupled to a circuit oscillator.

## Thursday, March 11, 2010

### The Quantum Random Walk

Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The number of optical elements required scales linearly with the number of steps. We measure walks with up to 6 steps and explore the quantum-to-classical transition by introducing tunable decoherence. Finally, we also investigate the effect of absorbing boundaries and show that decoherence significantly affects the probability of absorption.

## Wednesday, March 3, 2010

### An Invisible Quantum Tripwire

We present here a quantum tripwire, which is a quantum optical interrogation technique capable of detecting an intrusion with very low probability of the tripwire being revealed to the intruder. Our scheme combines interaction-free measurement with the quantum Zeno effect in order to interrogate the presence of the intruder without interaction. The tripwire exploits a curious nonlinear behavior of the quantum Zeno effect we discovered, which occurs in a lossy system. We also employ a statistical hypothesis testing protocol, allowing us to calculate a confidence level of interaction-free measurement after a given number of trials. As a result, our quantum intruder alert system is robust against photon loss and dephasing under realistic atmospheric conditions and its design minimizes the probabilities of false positives and false negatives as well as the probability of becoming visible to the intruder.

## Friday, February 26, 2010

### Observation of a kilogram-scale oscillator near its quantum ground state

We introduce a novel cooling technique capable of approaching the quantum ground state of a kilogram-scale system—an interferometric gravitational wave detector. The detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) operate within a factor of 10 of the standard quantum limit (SQL), providing a displacement sensitivity of 10−18 m in a 100 Hz band centered on 150 Hz. With a new feedback strategy, we dynamically shift the resonant frequency of a 2.7 kg pendulum mode to lie within this optimal band, where its effective temperature falls as low as 1.4 μK, and its occupation number reaches about 200 quanta. This work shows how the exquisite sensitivity necessary to detect gravitational waves can be made available to probe the validity of quantum mechanics on an enormous mass scale.

### Violation of the Leggett-Garg inequality with weak measurements of photons

By weakly measuring the polarization of a photon between two strong polarization measurements, we experimentally investigate the correlation between the appearance of anomalous values in quantum weak measurements, and the violation of realism and non-intrusiveness of measurements. A quantitative formulation of the latter concept is expressed in terms of a Leggett-Garg inequality for the outcomes of subsequent measurements of an individual quantum system. We experimentally violate the Leggett-Garg inequality for several measurement strengths. Furthermore, we experimentally demonstrate that there is a one-to-one correlation between achieving strange weak values and violating the Leggett-Garg inequality.

## Thursday, February 11, 2010

### Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature

Photosynthesis makes use of sunlight to convert carbon dioxide into useful biomass and is vital for life on Earth. Crucial components for the photosynthetic process are antenna proteins, which absorb light and transmit the resultant excitation energy between molecules to a reaction centre. The efficiency of these electronic energy transfers has inspired much work on antenna proteins isolated from photosynthetic organisms to uncover the basic mechanisms at play

^{1, }

^{2, }

^{3, }

^{4, }

^{5}. Intriguingly, recent work has documented

^{6, }

^{7, }

^{8}that light-absorbing molecules in some photosynthetic proteins capture and transfer energy according to quantum-mechanical probability laws instead of classical laws

^{9}at temperatures up to 180 K. This contrasts with the long-held view that long-range quantum coherence between molecules cannot be sustained in complex biological systems, even at low temperatures. Here we present two-dimensional photon echo spectroscopy

^{10, }

^{11, }

^{12, }

^{13}measurements on two evolutionarily related light-harvesting proteins isolated from marine cryptophyte algae, which reveal exceptionally long-lasting excitation oscillations with distinct correlations and anti-correlations even at ambient temperature. These observations provide compelling evidence for quantum-coherent sharing of electronic excitation across the 5-nm-wide proteins under biologically relevant conditions, suggesting that distant molecules within the photosynthetic proteins are ‘wired’ together by quantum coherence for more efficient light-harvesting in cryptophyte marine algae.

## Wednesday, February 3, 2010

### Coherent control in the classical limit: Symmetry breaking in an optical lattice

The quantum-to-classical transition of a symmetry-breaking coherent control scenario is computationally demonstrated in an optical lattice arrangement. Control is shown to survive in the classical limit and, for small effective ℏ, to be comparable in magnitude to quantum control. Moderate decoherence is seen to eliminate structure from the momentum space distribution, but not to cause loss of control. The proposed scenario is designed so as to be demonstrable experimentally in a moving or shaken one-dimensional optical lattice.