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DynamicalCasimir Effect

Diego A. R. Dalvit, T-DO/QC;dalvit@lanl.gov

What happens if you place twomirrors facing each otherin empty space? e naveanswer is nothing at all.

Surprisingly, both mirrors attract each otherdue to the presence of the electromagnetic

vacuum (Fig. 1). is phenomenon, nowcalled the Casimireffect, was predictedin 1948 by the Dutchtheoretical physicistHendri Casimir,and has been recently

measured at the15% accuracy levelusing cantilevers.A force of similarnature between aconducting planeand a conductingsphere has alsobeen measured withincreasing precisionusing torsionbalances, atomic

force microscopes,and micromechanicalresonators. Casimir forces are relevantfor nanotechnology because they affectthe operation of microelectromechanicalsystems. Also, the predicted existence of newinteractions with coupling comparable togravity but range in the micrometer rangeadds strong motivations to control theCasimir force at the highest level of accuracy.

When the Casimir plates are put in non-uniform accelerated motion, it is in principle

possible to create real photons out of vacuum.is effect is referred to in the literature asdynamical Casimir effect, or motion-inducedradiation. e most favorable setup forobserving it is a high quality microwave cavitywhere one of its mirrors is oscillating withone of the resonant frequencies of the cavity.In such a case, the number of photons insidethe cavity accumulates slowly and growsexponentially in time. Unfortunately, unlike

the static Casimir effect, an experimentalverification of the dynamical counterpartis still lacking. e main reason is thattypical resonance frequencies for microwavecavities are of the order of gigahertz, and itis of course very difficult to make a mirroroscillate at such high frequencies. At present,

alternative ideas are being pursued, such asswitching an effective mirror on and off at

very short intervals of time, changing thereflectivity of a semiconductor layer insidethe cavity by shining a pulsed laser beam onits surface.

We have studied the creation of photonsin 3D oscillating microwave cavities.e physical degrees of freedom of theelectromagnetic field are expressed interms of two independent scalar fields,the so-called Hertz potentials [1]. One ofthem corresponds to transverse electric(TE) modes, satisfying Dirichlet boundaryconditions on the moving mirror, while theother one corresponds to transverse magnetic(TM) modes and verifies (generalized)

Neumann boundary conditions. e rateof photo-production for the TM photons isin general larger than for TE photons. Wehave also studied transverse electromagnetic(TEM) modes, that appear in non-simplyconnected cavities, such as between twoconcentric hollow cylinders. is case reducesto a 1D problem for a scalar field with time-dependent boundary conditions (Fig. 2).

VACUUM

FLUCTUATIONS

CASIMIR PLATES

Figure 1

When two uncharged,perfectly conducting

parallel plates are facingeach other, they modify

the mode structure ofthe electromagnetic

vacuum. As a result,

there is a net attractiveforce between them, the

so-called Casimir force.

RESEARCH HIGHLIGHTS 2005 THEORETICAL DIVISION

T-DO/QC QUANTUM COMPUTING

8/3/2019 Diego A. R. Dalvit- Dynamical Casimir Effect

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Finally, we have started the theoreticalmodeling of a proposed experiment tomeasure the dynamical Casimir effect withthe semiconductor of time-dependentreflectivity. We have shown that the proposedsetup offers several advantages over the caseof motion-induced radiation arising frommoving mirrors, such as much faster photo-

production rates and milder fine tuningproblems [2].

[1] M. Crocce, D.A.R. Dalvit, F.C. Lombardo,and F.D. Mazzitelli, Hertz PotentialsApproach to the Dynamical Casimir Effect inCylindrical Cavities of Arbitraty Section, toappear inJournal Opt. B (2005);quant-ph/0411106.[2] M. Crocce, D.A.R. Dalvit, F.C. Lombardo,and F.D. Mazzitelli, Model for ResonantPhoton Creation in a Cavity with Time-Dependent Conductivity, Phys. Rev. A70,

033811 (2004).

T

Figure 2

Energy density profilefor a 1D cavity whose

length oscillates at

the fourth resonantfrequency of the static

cavity. Real photonsare generated inside the

cavity, with a structure

of four peaks that moveback and forth within

the cavity. Te totalenergy inside the cavity

increases exponentiallyin time at the expense of

the energy supplied to

the mirrors to keepthem oscillating.

0.0 0.2 0.4 0.6 0.8 1.0

z / Lz

50.0

0.0

50.0

100.0

150.0

200.0

250.0

Lz2

.

A U.S. DEPARTMENT OF ENERGY LABORATORY LA-UR-05-1500 APRIL 2005