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that due to the interference of the two laser beams, V 0 isfour times larger than V trap if the laser power and beamparameters of the two interfering lasers are equal.

Periodic potentials in two dimensions can be formedby overlapping two optical standing waves along differ-ent, usually orthogonal, directions. For orthogonal po-larization vectors of the two laser fields, no interferenceterms appear. The resulting optical potential in the cen-ter of the trap is then a simple sum of a purely sinusoidalpotential in both directions.

In such a two-dimensional optical lattice potential, at-oms are confined to arrays of tightly confining one-dimensional tubes !see Fig. 4"a#$. For typical experimen-tal parameters, the harmonic trapping frequencies alongthe tube are very weak "on the order of 10–200 Hz#,while in the radial direction the trapping frequencies canbecome as high as up to 100 kHz. For sufficiently deeplattice depths, atoms can move only axially along thetube. In this manner, it is possible to realize quantumwires with neutral atoms, which allows one to studystrongly correlated gases in one dimension, as discussedin Sec. V. Arrays of such quantum wires have been real-ized "Greiner et al., 2001; Moritz et al., 2003; Kinoshita etal., 2004; Paredes et al., 2004; Tolra et al., 2004#.

For the creation of a three-dimensional lattice poten-tial, three orthogonal optical standing waves have to beoverlapped. The simplest case of independent standingwaves, with no cross interference between laser beamsof different standing waves, can be realized by choosingorthogonal polarization vectors and by using slightly dif-ferent wavelengths for the three standing waves. The

resulting optical potential is then given by the sum ofthree standing waves. In the center of the trap, for dis-tances much smaller than the beam waist, the trappingpotential can be approximated as the sum of a homoge-neous periodic lattice potential

V p"x,y,z# = V 0"sin2 kx + sin2 ky + sin2 kz# "36#

and an additional external harmonic confinement due tothe Gaussian laser beam profiles. In addition to this, aconfinement due to the magnetic trapping is often used.

For deep optical lattice potentials, the confinement ona single lattice site is approximately harmonic. Atomsare then tightly confined at a single lattice site, with trap-ping frequencies !0 of up to 100 kHz. The energy "!0=2E r"V 0 / E r#1/2 of local oscillations in the well is on theorder of several recoil energies E r="2k2 /2m, which is anatural measure of energy scales in optical lattice poten-tials. Typical values of E r are in the range of severalkilohertz for 87Rb.

Spin-dependent optical lattice potentials. For large de-tunings of the laser light forming the optical latticescompared to the fine-structure splitting of a typicalalkali-metal atom, the resulting optical lattice potentialsare almost the same for all magnetic sublevels in theground-state manifold of the atom. However, for morenear-resonant light fields, situations can be created inwhich different magnetic sublevels can be exposed tovastly different optical potentials "Jessen and Deutsch,1996#. Such spin-dependent lattice potentials can, e.g.,be created in a standing wave configuration formed bytwo counterpropagating laser beams with linear polar-ization vectors enclosing an angle # "Jessen and Deutsch,1996; Brennen et al., 1999; Jaksch et al., 1999; Mandel etal., 2003a#. The resulting standing wave light field can bedecomposed into a superposition of a $+- and a$−-polarized standing wave laser field, giving rise to lat-tice potentials V +"x ,##= V 0 cos2"kx+# /2# and V −"x ,##= V 0 cos2"kx−# /2#. By changing the polarization angle #,one can control the relative separation between the twopotentials %x= "# /&#'x /2. When # is increased, both po-tentials shift in opposite directions and overlap againwhen #=n&, with n an integer. Such a configuration hasbeen used to coherently move atoms across lattices andrealize quantum gates between them "Jaksch et al., 1999;Mandel et al., 2003a, 2003b#. Spin-dependent lattice po-tentials furthermore offer a convenient way to tune in-teractions between two atoms in different spin states. Byshifting the spin-dependent lattices relative to eachother, the overlap of the on-site spatial wave functioncan be tuned between zero and its maximum value, thuscontrolling the interspecies interaction strength within arestricted range. Recently, Sebby-Strabley et al. "2006#have also demonstrated a novel spin-dependent latticegeometry, in which 2D arrays of double-well potentialscould be realized. Such “superlattice” structures allowfor versatile intrawell and interwell manipulation possi-bilities "Fölling et al., 2007; Lee et al., 2007; Sebby-Strabley et al., 2007#. A variety of lattice structures canbe obtained by interfering laser beams under different

(a)

(b)

FIG. 4. "Color online# Optical lattices. "a# Two- and "b# three-dimensional optical lattice potentials formed by superimposingtwo or three orthogonal standing waves. For a two-dimensional optical lattice, the atoms are confined to an arrayof tightly confining one-dimensional potential tubes, whereasin the three-dimensional case the optical lattice can be ap-proximated by a three-dimensional simple cubic array oftightly confining harmonic-oscillator potentials at each latticesite.

896 Bloch, Dalibard, and Zwerger: Many-body physics with ultracold gases

Rev. Mod. Phys., Vol. 80, No. 3, July–September 2008

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one-dimensional organic with a half-filled !-electron band.Strong on-site Coulomb repulsion leads to a Mott-insulatingstate with a transition to a dimerized spin-Peierls (SP) statebelow TSP ¼ 395 K due to a strong spin-lattice interaction.

Photoexcitation creates localized carriers which destabilizethe magnetic state resulting in melting of the spin-Peierlsphase in<400 fs. Spectroscopic evidence for this is shown inFig. 20. The peak at "1 eV (solid line) in Fig. 20(a) is acharge-transfer transition, while the circles are photocurrentmeasurements of the onset of which is "0:5 eV above theexcitonic charge-transfer transition and corresponds to thecreation of unbound electron-hole pairs. The photoinduced(150 fs, 1.55 eV pulses) absolute reflectivity change !R as afunction of probe photon energy at various time delays isshown in Fig. 20(b). There are two features. A positive !R atlower energies is ascribed to small polarons. The ultrafastdecrease of!R between 0.75 and 1.75 eV is spectrally similarto dR=dE [see Fig. 20(c)] determined using the static spec-trum in Fig. 20(a). This differential response is associatedwith a decrease in dimerization based on analysis of thetemperature-dependent redshift of the charge-transfer peakwhich follows the changes in the x-ray reflection intensityassociated with dimerization. Thus, the picture that emergesis that photoexcitation leads to the formation of polaronswhich break spin-singlet dimers that, in turn, destabilize thespin-Peierls phase. Analysis of the oscillatory time-domainresponse of !R=R (not shown) indicates that this ‘‘melting’’of the spin-Peierls phase initiates a coherent excitation of the20 cm#1 mode corresponding to the lattice distortion asso-ciated with dimerization.

Further ultrafast studies using shorter pulses (sub-10 fs)comparing the response of the spin-Peierls compound K-TCNQ with a pure Mott analog ðBEDT-TTFÞðF2TCNQÞ

[where BEDT-TTF or ET stands for bis-(ethylenedithio)tetrathiafulvalene] show remarkably different responses atearly times (Okamoto et al., 2007; Wall et al., 2009;Uemura et al., 2010), as shown in Fig. 21. These results

ν

FIG. 19 (color online). Depiction of a photoinduced phase tran-sition showing the potential energy as a function of a generalizedstructural coordinate. The basic idea is the so-called ‘‘dominoeffect’’: Photoexcitation initiates a structural change which, inturn, drives an electronic phase transition with an order parameterdifferent from that in the ground state. The energy barrier to obtainthe new long-range (though likely metastable) ordered phase isgreater than kbT. The dashed arrows labeled (i) and (ii) depictelectronic and vibrational routes toward inducing a phase transition.From Nasu, 2004.

R∆R

dR/d

E

Photon energy (eV)

Pho

tocu

rren

t (a.

u.)

K-TCNQ pump (a)

(b)

(c)

FIG. 20 (color online). (a) Reflectivity and photocurrent measuredon K-TCNQ as a function of frequency taken at room temperaturewhich is well below TSP ¼ 395 K. The peak at 1 eV corresponds toan excitonic charge-transfer excitation and the onset of a photo-current response at "0:5 eV above this is due to the excitation ofunbound electron-hole pairs. (b) Spectral dependence of photo-induced absolute reflectivity change !R at various time delaysfollowing excitation. The lowest-energy peak arises from polaronformation while the change in the charge-transfer peak suggests‘‘melting’’ of the spin-Peierls phase. (c) The derivative of reflectiv-ity in (a) with respect to photon energy shows a similar spectralresponse to the time-resolved data which supports the interpretationof the dynamics. From Okamoto et al., 2006.

FIG. 21 (color online). Ultrafast dynamics measured on K-TCNQand ðBEDT-TTFÞðF2TCNQÞ. The spin-Pierels compound K-TCNQ(black line) shows a structural bottleneck in that the rise time is320 fs while the Mott-Hubbard compound K-TCNQ (gray line),with a rise time of 19 fs, does not exhibit a structural bottleneck. Inaddition, the oscillations in the K-TCNQ data results from thecoherent excitation of vibrational modes as shown in the inset.From Wall et al., 2009.

496 Basov et al.: Electrodynamics of correlated electron materials

Rev. Mod. Phys., Vol. 83, No. 2, April–June 2011

Basov et al. , Rev. Mod. Phys.83,431(2011).

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<latexit sha1_base64="+cSPuw09pGK7cmjMjoKqJDbaat4=">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</latexit><latexit sha1_base64="+cSPuw09pGK7cmjMjoKqJDbaat4=">AAADFXichVFNa9RQFD2NX3X86KgbwU1wqMwsOt4MgiIIVTcu++G0hck0JJk300fzkpC8Gaxh/oB/oAtXCi7E3+BKERHElYv+BHEjVBDFhTeZFNHieEPeu/e8c+67714vDmSqifZmjCNHjx0/MXuycur0mbNz1XPn19JomPii7UdBlGx4bioCGYq2ljoQG3EiXOUFYt3bvpufr49EksoovK93YtFV7iCUfem7miGn2rM9ld0e13Xj1sRzyLTFg9i0A9HXHXOhrhe0Q43N1tV6S2+2nMxOlNkbqnjcMO1EDrZ01/aj9IBvR0oM3FJ0QHCqNWpSYeZhxyqdGkpbiqrvYaOHCD6GUBAIodkP4CLlrwMLhJixLjLGEvZkcS4wRoW1Q2YJZriMbvM64KhToiHHec60UPt8S8B/wkoT8/SRntM+vaUX9Il+/jNXVuTIa9nh3ZtoRezMPbq4+u2/KsW7xtZv1RSFx5W5HAtW5PxpTDWVkb9fo48bxbsl9yEukLwj/qSW0cPd/dWbK/PZFXpKn7kXT2iPXnE3wtFX/9myWHmMCg/T+nt0h521VtOiprV8rbZ4pxzrLC7hMuo8u+tYxD0soc33vsMXfMcPY9d4abw23kyoxkypuYA/zPjwC4aWvsc=</latexit><latexit sha1_base64="+cSPuw09pGK7cmjMjoKqJDbaat4=">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</latexit><latexit sha1_base64="+cSPuw09pGK7cmjMjoKqJDbaat4=">AAADFXichVFNa9RQFD2NX3X86KgbwU1wqMwsOt4MgiIIVTcu++G0hck0JJk300fzkpC8Gaxh/oB/oAtXCi7E3+BKERHElYv+BHEjVBDFhTeZFNHieEPeu/e8c+67714vDmSqifZmjCNHjx0/MXuycur0mbNz1XPn19JomPii7UdBlGx4bioCGYq2ljoQG3EiXOUFYt3bvpufr49EksoovK93YtFV7iCUfem7miGn2rM9ld0e13Xj1sRzyLTFg9i0A9HXHXOhrhe0Q43N1tV6S2+2nMxOlNkbqnjcMO1EDrZ01/aj9IBvR0oM3FJ0QHCqNWpSYeZhxyqdGkpbiqrvYaOHCD6GUBAIodkP4CLlrwMLhJixLjLGEvZkcS4wRoW1Q2YJZriMbvM64KhToiHHec60UPt8S8B/wkoT8/SRntM+vaUX9Il+/jNXVuTIa9nh3ZtoRezMPbq4+u2/KsW7xtZv1RSFx5W5HAtW5PxpTDWVkb9fo48bxbsl9yEukLwj/qSW0cPd/dWbK/PZFXpKn7kXT2iPXnE3wtFX/9myWHmMCg/T+nt0h521VtOiprV8rbZ4pxzrLC7hMuo8u+tYxD0soc33vsMXfMcPY9d4abw23kyoxkypuYA/zPjwC4aWvsc=</latexit>

freq:

tshift:

tdump:

VecPotW, L: ���

��$!$�

�"����38��N?AU

9

Norm.dat��,48MUQ���>��→SKGTX�"��)5=0+':*&12&<(8�!

SS.dat��,48BLUCX%� ��65>��

##_cisajs_step%%.dat��,48OneBodyG3� -/��ETXW#�8����>��

65

���I@VDJT��79%��38ODJUPHWFRU4$�>��.</;8N?AU potential.dat)��

OutputI@VDJT

��: Gaussian���

10

model = "Hubbard"method = "Time-Evolution"lattice = "Square"a0W = 2a0L = 2a1W = 2a1L = -2lanczos_max = 5000dt = 0.001PumpType = "Pulse Laser"t = 1.0U = 10.0nelec = 82Sz = 0EigenvecIO = "in"tshift = 5.0tdump = 1.5freq = 8.0VecPotW = 0.1VecPotL = 0.1

����hHi

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-4

-2

0

2

4

0 2 4 6 8 10

Time

A0 = (0.1, 0.1),

!/t = 8<latexit sha1_base64="WaTmssL0AOL9XoLCfGbET9rgkBQ=">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</latexit><latexit sha1_base64="WaTmssL0AOL9XoLCfGbET9rgkBQ=">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</latexit><latexit sha1_base64="WaTmssL0AOL9XoLCfGbET9rgkBQ=">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</latexit><latexit sha1_base64="WaTmssL0AOL9XoLCfGbET9rgkBQ=">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</latexit>

A0 = (2, 2),

!/t = 25<latexit sha1_base64="cN2NvcpxcHyG+zt0RbtXqqeQpJ0=">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</latexit><latexit sha1_base64="cN2NvcpxcHyG+zt0RbtXqqeQpJ0=">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</latexit><latexit sha1_base64="cN2NvcpxcHyG+zt0RbtXqqeQpJ0=">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</latexit><latexit sha1_base64="cN2NvcpxcHyG+zt0RbtXqqeQpJ0=">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</latexit>

A(t) = A0 exp⇥�(t� t0)

2/(2t2dump)⇤cos [!(t� t0)]

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11

• ��!.+1%2$������http://issp-center-dev.github.io/HPhi/manual/userguide_HPhi_ja.pdf